# The Best Thresholds for Rapid Identification of Episodic and Chronic
Homeless Shelter Use

Geoffrey Messier
University of Calgary
2500 University Dr. NW, Calgary, AB, Canada, T2N 1N4
<EMAIL_ADDRESS>Leslie Tutty
University of Calgary
2500 University Dr. NW, Calgary, AB, Canada, T2N 1N4
<EMAIL_ADDRESS>Caleb John
University of Calgary
2500 University Dr. NW, Calgary, AB, Canada, T2N 1N4
<EMAIL_ADDRESS>
###### Abstract

This paper explores how to best identify clients for housing services based on
their homeless shelter access patterns. We focus on counting the number of
shelter stays and episodes of shelter use for a client within a time window.
Thresholds are then applied to these values to determine if that individual is
a good candidate for housing support. Using new housing referral impact
metrics, we explore a range of threshold and time window values to determine
which combination both maximizes impact and identifies good candidates for
housing as soon as possible. New insights are also provided regarding the
characteristics of the “under-the-radar” client group who are typically not
identified for housing support.

Keywords: chronic homelessness, episodic homelessness, housing first services,
data analysis

##  1 Introduction

An emergency homeless shelter sees a diversity of clients who access the
shelter in different ways and require different services. Shelter access is
often characterized in terms of total stays and number of episodes [13]. The
analysis of shelter stay and episode data has led to the discovery of three
different types of shelter access patterns: transitional/temporary, episodic
and chronic. The majority of new clients are transitional and exit shelter
after a relatively short time. Episodic clients access shelter intermittently
over a long period and chronic clients access shelter very regularly over a
long period. These three groups have been identified using cluster analysis on
shelter access data from a number of North American cities [13, 6, 3, 12].

The original purpose of shelter stay and episode data was to gain a better
understanding of the homeless population. However, it is now also increasingly
being used to help guide program delivery. Housing First services have been a
priority for the Canadian federal government’s Homelessness Partnering
Strategy since 2013 [8]. Housing First is a recovery-oriented approach to
quickly and successfully connect individuals and families experiencing
homelessness to permanent housing without preconditions and barriers to entry,
such as sobriety, treatment or service participation requirements [10].
Housing chronically and episodically homeless individuals is one of the
priorities of Housing First programming [9, 2]. A number of definitions for
chronic and episodic homelessness have been developed that can applied to
shelter access data, used to identify these individuals and then connect them
to housing supports [4, 5, 16, 7].

The purpose of this paper is to examine how best to use stay/episode threshold
tests to identify clients for housing services based on their shelter access
patterns. While it is only one of the tools that should be use to triage
clients for housing services [2], shelter access data analysis is important
since it has the potential to spot clients who are in need help and might
otherwise escape notice. This is particularly true in very busy shelters where
staff may not have personal knowledge of all clients.

There are two priorities when identifying an individual for housing supports:
selecting the clients in greatest need of housing and finding them as quickly
as possible after they first enter shelter. The primary contribution of this
paper is to create new threshold-based tests for chronic and episodic shelter
use with these two priorities in mind. Using 13 years of anonymized client
data from a major North American shelter, we will demonstrate that our
approach is able to identify clients for housing services almost 200 days
sooner than existing definitions for chronic homelessness.

In the following, Section 2 describes the dataset used for this study and
cluster analysis is used in Section 3 to demonstrate that our data is
representative of homeless populations in other major urban centres. Section 4
presents the analysis we use to develop our tests which we then compare to
existing definitions for chronic homelessness in Section 5. Section 6 provides
some insight into the individuals who are not identified for housing support
and concluding remarks are made in Section 7.

##  2 Data Set

This is a secondary data analysis performed on anonymized shelter stay records
collected at the Calgary Drop-In Centre (DI) between July 1, 2007 and January
20, 2020. The data anonymization and client privacy protocol used during this
study was approved by the University of Calgary Conjoint Faculties Research
Ethics Board. The dataset consists of 5,431,521 entries for 34,577 unique
client profiles.

Each time a shelter client accesses day sleep or night sleep facilities at the
DI, an entry is created in the database with a timestamp and the unique
identification number of the client. For the purposes of this study, a single
stay is defined as a 24 hour period where a client accesses day sleep
services, night sleep services or both. An episode is a series of stays where
the separation between consecutive stay dates is less than 30 days [4].

As discussed in [13], studies that examine periods of time in shelter suffer
from the censoring of client access patterns that begin before the start of
the data record (left-censoring bias) and continue after the end of the data
record (right-censoring-bias). Following the approach in [13], we minimize the
effect of left and right censoring bias by only including clients who first
appear in the data after July 1, 2009 and prior to January 20, 2018. A total
of 18,398 client profiles meet this inclusion criterion (53.2% of the original
dataset population).

##  3 Cluster Analysis

In order for the analysis and conclusions presented in this paper to be
generally relevant, it is important to establish that our dataset is
representative of homeless populations in other jurisdictions. To compare our
data with existing populations, we perform a cluster analysis in this section
to study the nature of our transitional, episodic and chronic populations.

Utilizing the definition for stays and episodes described in Section 2, the
total number of stays and episodes experienced by each of the $N$ = 18,398
clients included in this study is calculated. This data is then analyzed using
the $k$-means clustering algorithm [11, 13, 3, 12] where $k=3$ clusters is
assumed. Z-score variable standardization is used to normalize the stay and
episode data to have zero mean and unit variance prior to clustering [14]. The
average stay and episode values for each cluster are given in Table 1. Similar
to [3, 12], we validate our clusters by verifying that the differences between
the means of our centroids are statistically significant. Since this is a
multi-variable analysis, we utilize Hotelling’s t-squared test [1]. All
comparisons of the means provided in Table 1 using Hotelling’s test yield a
p-value of less than 0.001.

Group | Average Total Episodes | Average Total Stays | Proportion of Population
---|---|---|---
Transitional | 1.8 | 30.3 | 85.2% (15675/18398)
Episodic | 9.2 | 167.0 | 11.9% (2184/18398)
Chronic | 3.7 | 1273.1 | 2.9% (539/18398)
Table 1: Statistical averages for cluster groups.

To verify that our dataset is representative, the results in Table 1 can be
compared to cluster analysis studies conducted for other North American cities
[13, 6, 3], including a multi-shelter study conducted in Calgary [12]. When
comparing with the Canadian cities, the proportions of chronic, episodic and
transitional clients are similar to within a few percentage points. The
average number of episodes and stays are also similar with exception of the
1273.1 average total stays for chronic clients. The most similar average
number of chronic stays are 927.1 and 769.3 for the multi-shelter Calgary
study and Ottawa study, respectively. Our larger value can be explained by the
fact that the DI is the largest shelter in Calgary and, before the advent of
Housing First programming, had a number of very regular and long term clients.

When comparing to cities in the United States, our results are most similar to
[13]. The results in [6] have a higher proportion of chronic clients (in some
cases up to 20%) and a higher number of stays in shelter for transitional
users (over 100 for Philadelphia and Massachusetts). We do not think these
differences are large enough to invalidate the main conclusions of our work
for American cities since the variation between Table 1 and the results in [6]
is similar to the variation observed between [6] and [13, 3, 12].

##  4 Identifying Chronic Shelter Users

One way to identify a chronic shelter user is to see if they satisfy one of
the many definitions of chronic homelessness [7, 16, 5, 4]. While these
definitions differ in minor ways, they are all variations of applying a
threshold test to the number of shelter stays or episodes of shelter use that
occur within a time window. For example, an individual satisfies the Canadian
federal definition of homelessness if they have 180 or more shelter stays in
one year (a threshold of 180 stays and a time window of 365 days).

When designing a test to identify chronic shelter users for housing support,
the test should maximize the impact of each housing intervention. Section 4.1
presents a new way to examine historical shelter data to quantify how much
time in shelter could be saved when a client is referred to a housing program.
Section 4.2 then evaluates a large number of time window and stay/episode
threshold values to find the combination that maximizes the impact of housing
referrals while identifying clients for assistance as quickly as possible.

We will maintain separate definitions for chronic and episodic shelter
clients. While some definitions test separately for chronic and episodic
clients [7, 16], they then lump these clients together and call them all
“chronic”. We choose to maintain separate tests for episodic and chronic
shelter users since they exhibit very different characteristics [13, 3] and
could benefit from different types of support.

###  4.1 Evaluating the Impact of a Housing Intervention

As noted in Section 1, one priority when delivering housing services is
achieving high program efficiency which is defined as ensuring resources are
allocated to those who need it most [15]. This could be achieved by using a
very conservative test for chronic shelter use that requires a long period in
shelter before triggering a housing referral. However, this approach is at
odds with our second priority of quickly providing clients with assistance
before the difficult conditions experienced during a long period in shelter
have an adverse effect on their mental and physical health.

Finding a test for chronic/episodic shelter use that achieves the best
tradeoff between program efficiency and rapid intervention requires the right
performance metric. In the past, the best test for chronic homelessness has
been selected as the one identifying the group that consumes the highest
percentage of total shelter stays [4]. While this is a good metric for program
efficiency, it does not account for how quickly those clients are identified.

To address this point, we propose a metric that evaluates how much a housing
referral reduces a client’s time in shelter. We define referral date as the
point in time where a test for chronic or episodic shelter use is satisfied in
a client’s historic shelter access timeline. We make the idealized assumption
that the client receives a “perfect” housing referral on their referral date.
This means the client transitions directly to housing on the same day they are
identified by the test and does not return to shelter.

We then calculate the shelter stays saved and shelter tenure reduction for
that client due to the housing referral. Consistent with Section 2, a stay is
defined as a 24 hour period where the client accesses shelter sleep services
one or more times. The tenure of a client in shelter is defined as the number
of days between the first and last day the client appears in the shelter
record. To determine stays saved by a housing referral, we add up all shelter
stays that remain in the client’s timeline after the referral date. To
determine the tenure reduction achieved by a housing referral, we count the
number of days between the referral date and the last day they appear in their
shelter access record.

For example, consider a hypothetical client in the DI dataset that stays in
shelter on April 10, 12, 13, 20, 22 and 30. Assume we apply a test to that
access pattern that identifies the client as chronic on April 13. April 13
would be the client’s referral date and we assume they leave shelter and move
into a house on that day. Since there are 3 more stays in the timeline (April
20, 22 and 30), the number of stays saved by the referral is 3. Since the
final time the client actually accesses shelter is April 30, the tenure
reduction for the client is 17 days.

While this metric is clearly ideal, it is very effective for evaluating the
tradeoff between program efficiency and speed of identification. For example,
a very conservative test that only identifies a client after a long time in
shelter will have a low stays saved/tenure reduction score since there will
not be much time left in the client’s shelter timeline by the time they are
identified for a referral. Conversely, a definition that identifies clients
too early will also score low since it will start to identify transitional
clients that have a small number of shelter stays in their timeline.

We believe that it is important to evaluate both stays saved and reduction in
tenure. The number of stays saved maps easily to shelter system cost savings
since stays are directly linked to the number of beds a shelter must operate.
Calculating reduction in tenure, we argue, is a better measure of social cost.
An individual who interacts with an emergency shelter for an extended period,
even if that interaction is very intermittent, is most likely in some level of
distress for that entire period and not just the days physically spent in
shelter.

###  4.2 Finding the Best Test

While existing definitions for chronic homelessness often make intuitive
sense, they have not been proven to be “best” in any quantifiable way. In this
section, we evaluate several different combinations of stay/episode threshold
and time window values to find the combination that achieves the best tradeoff
between program efficiency and speed of identification.

For chronic shelter use, we evaluate the performance of all possible
combinations of time windows equal to 30, 90, 180, 365 and 547 days and stay
thresholds equal to 50%, 75% and 90% of the time window being applied (a total
of 15 threshold/window combinations). For episodic shelter use, we evaluate
all combinations of time windows equal to 30, 90, 180, 365 and 547 days and
episode thresholds equal to 2, 3, 4 and 5 episodes (a total of 20
threshold/window combinations). We choose to evaluate the performance of the
chronic test in terms of average stays saved per housing referral since
chronic clients make the heaviest use of system resources. Episodic test
performance is evaluated in terms average tenure reduction per housing
referral since that emphasizes the extended period of time episodic clients
may be in distress.

Tables 2 and 3 show the top ten performing window/threshold combinations for
the chronic and episodic tests, respectively. The tables also include the
number of clients identified, percentage of total clients identified and the
median time to identification.

Window (days)/ |  | Avg. Stays Saved | Median ID Time
---|---|---|---
Threshold (stays) | N | per Referral | (days)
547/492 | 415 (2.3%) | 721.4 | 538.0
365/328 | 594 (3.2%) | 687.9 | 376.5
547/410 | 661 (3.6%) | 656.6 | 496.0
365/273 | 904 (4.9%) | 619.5 | 350.5
180/162 | 1075 (5.8%) | 588.4 | 222.0
547/273 | 1138 (6.2%) | 555.7 | 421.5
180/135 | 1583 (8.6%) | 504.4 | 188.0
365/182 | 1536 (8.3%) | 499.7 | 287.0
90/81 | 1815 (9.9%) | 471.2 | 137.0
180/90 | 2370 (12.9%) | 416.6 | 142.0
Table 2: Window/threshold performance for chronic detection. Window (days)/ |  | Avg. Tenure Reduction | Median ID Time
---|---|---|---
Threshold (episodes) | N | per Referral (days) | (days)
180/4 | 310 (1.7%) | 932.9 | 731.5
365/5 | 618 (3.4%) | 906.6 | 748.5
365/3 | 3476 (18.9%) | 872.8 | 313.0
547/5 | 1246 (6.8%) | 868.1 | 666.5
180/3 | 1903 (10.3%) | 864.7 | 460.0
547/4 | 2331 (12.7%) | 858.1 | 485.0
365/4 | 1581 (8.6%) | 857.0 | 569.0
547/3 | 4201 (22.8%) | 854.7 | 367.0
90/2 | 4277 (23.2%) | 829.7 | 181.0
90/3 | 275 (1.5%) | 829.3 | 663.0
Table 3: Window/threshold performance for episodic detection.

When deciding which window/threshold combinations to select from Tables 2 and
3, we are mindful of the priority of identifying clients for assistance as
quickly as possible. In Table 2, a window of 547 days and a threshold of 492
stays has the best performance in terms of stays saved per housing referral.
This test maximizes stays saved since it selects only the 2.3% of clients who
are heavy, long term shelter users. However, this test is unacceptable because
it takes a median time of 538 days (approx. 1.5 years) to identify a client
for referral.

If we examine Table 2 at a higher level, we can see that even the worst
performing test still saves an impressive 416.6 shelter stays per referral.
Since all the tests are very high impact, we are free to choose the test that
also offers rapid identification of chronic shelter users. A time window of 90
days and a stay threshold of 81 offers a median time to identification of only
137 days (less than 5 months). This test ranks 9th but still selects a cohort
of clients for referrals that save an average of 471.2 stays each time a
client is placed in housing.

When examining the episodic results in Table 3, the tenure reduction values
are very strong for all of the window/threshold combinations. Therefore, we
select the 90 day window and 2 episode threshold combination as achieving a
good tradeoff between impact and speed of detection. This test ranks 9th but
still reduces a client’s tenure of shelter interaction by an average of 829.7
days (2.4 years) when that client is referred to housing.

To summarize, we would like to propose the RAPid IDentification (RAPID) test
for chronic shelter use (RAPID-Chronic) as identifying any client with 81 or
more stays in shelter in a 90 day period. The RAPID test for episodic shelter
use (RAPID-Episodic) identifies any client with 2 or more episodes of shelter
access in a 90 day period.

##  5 Evaluation and Results

In this section, we compare the RAPID tests to existing definitions for
chronic homelessness. We select the following definitions as being generally
representative of the homelessness serving sector and relevant to our local,
provincial and national contexts:

  * •

Government of Canada (GoC): “individuals who are currently experiencing
homelessness and who meet at least 1 of the following criteria: they have a
total of at least 6 months (180 days) of homelessness over the past year or
they have recurrent experiences of homelessness over the past 3 years, with a
cumulative duration of at least 18 months (546 days)” [7]

  * •

Government of Alberta (GoA): “A person or family is considered chronically
homeless if they have either been continuously homeless for a year or more, or
have had at least four episodes of homelessness in the past three years.” [16]

In the following, Section 5.1 presents the demographics of the individuals
selected for housing by the RAPID, GoC and GoA definitions. Section 5.2
compares how each definition performs in terms of stays saved, tenure
reduction and time to identification.

###  5.1 Clients Identified for Support

The client group statistics presented in this section include total shelter
stays, total episodes of shelter access, tenure of shelter interactions and
shelter usage percentage (total stays divided by tenure). Each table also
indicates the total coverage of a definition (number of clients identified).
The statistics of the clients flagged by the GoC and GoA are given in Tables
4, and 5, respectively. The RAPID-Chronic and RAPID-Episodic tests are shown
in Tables 6 and 7, respectively.

The results in Table 4 indicate that the GoC definition selects primarily
chronic clients. It is interesting to note that the intention of the GoC
definition was also to lump in episodic shelter users by including a second
stay count threshold for a three year period. However, this second test still
selects primarily chronic clients. In contrast, the GoA test lumps together
clients that satisfy either a stay count test or episode test. This does
effectively group episodic and chronic users together. As a result, Table 5
shows a higher percentage of clients selected, lower values for total stays,
higher episode counts and lower shelter usage percentages.

The RAPID-Chronic results in Table 6 are most similar to the GoC definition in
terms of shelter usage percentage, tenure and episode counts. The values in
Table 7 for RAPID-Episodic reflect the primarily episodic clients selected by
this test with low stay counts but high tenure and episode counts.

| Mean | Median | 90th Percentile
---|---|---|---
Total Stays | 702.7 | 522.0 | 1430.0
Total Episodes | 4.4 | 3.0 | 9.0
Tenure (days) | 1564.1 | 1439.0 | 2940.0
Usage Percentage | 53.0% | 48.6% | 95.8%
Coverage: 1549/18398 (8.4%)
Table 4: Government of Canada definition. | Mean | Median | 90th Percentile
---|---|---|---
Total Stays | 438.6 | 216.0 | 1128.0
Total Episodes | 7.4 | 7.0 | 14.0
Tenure (days) | 1672.2 | 1592.0 | 2974.0
Usage Percentage | 28.3% | 14.1% | 84.1%
Coverage: 2443/18398 (13.3%)
Table 5: Government of Alberta definition. | Mean | Median | 90th Percentile
---|---|---|---
Total Stays | 601.0 | 411.0 | 1329.0
Total Episodes | 4.0 | 3.0 | 9.0
Tenure (days) | 1399.9 | 1241.0 | 2837.0
Usage Percentage | 53.1% | 49.1% | 96.2%
Coverage: 1815/18398 (9.9%)
Table 6: RAPID-Chronic test. | Mean | Median | 90th Percentile
---|---|---|---
Total Stays | 136.9 | 39.0 | 376.0
Total Episodes | 6.3 | 5.0 | 12.0
Tenure (days) | 1308.4 | 1149.0 | 2763.0
Usage Percentage | 11.2% | 5.2% | 30.4%
Coverage: 4277/18398 (23.2%)
Table 7: RAPID-Episodic test.

###  5.2 Definition Performance Comparison

Table 8 compares the different definitions in terms of number of clients
identified, stays saved per referral, tenure reduction per referral, average
time to identification and median time to identification. The RAPID results
are generated by applying both the RAPID-Chronic and RAPID-Episodic tests to
each client in the DI dataset and then classifying them according to whichever
test is satisfied earliest in the client’s timeline. As a result, the total
clients identified by RAPID in Table 8 is less than the sum of clients in
Tables 6 and 7 since some clients satisfy both RAPID-Chronic and RAPID-
Episodic.

| Clients | Stays Saved | Tenure Reduction | Mean Time | Median Time
---|---|---|---|---|---
| Identified | per Referral | per Referral (days) | to ID (days) | to ID (days)
Government of Alberta | 2443 (13.3%) | 264.8 | 914.2 | 609.8 | 365.0
Government of Canada | 1549 (8.4%) | 498.4 | 1007.9 | 555.2 | 285.0
RAPID | 5507 (30.0%) | 194.8 | 874.4 | 402.2 | 98.0
Table 8: Definition performance comparison.

With a median time to identification of only 98 days or just over 3 months, we
think that the RAPID tests are the clear choice for housing program delivery.
The next quickest definition requires that a client remain in shelter for 285
days before being identified for support. While the RAPID tests result in the
lowest number of stays saved and lowest tenure reduction in Table 8, they
still have an impressive impact with an average number of stays saved per
referral of 194.8 and an average tenure reduction per referral of 874.4 days.
Clearly, RAPID does a good job of avoiding short term transitional shelter
users and finding high impact clients to connect to housing services.

Since RAPID identifies the highest proportion of clients, one possible concern
is that the RAPID tests will flag too many clients and overload housing
programs with potential candidates. When applied to the DI dataset, RAPID
identifies an average of just over 44 individual for housing services per
month. The current housing programs at the Calgary Drop-In Centre have
successfully been able to house approximately this many clients [5].
Therefore, we believe that the number of clients identified by RAPID should
fall within the capacity of most housing programs. It should also be stressed
that clients identified by RAPID are not necessarily automatically placed in a
home. As discussed in Section 1, these tests should be considered only one
component of a housing program that includes discussions with each client to
determine how best to support their exit from the shelter system.

Finally, we point out that Table 8 is a dramatic illustration of the potential
impact of Housing First services. Regardless of which definition is used,
housing referrals have the potential to save many hundreds of shelter stays
and, in some cases, over 1,000 days of tenure in shelter per referral.

##  6 Who are we missing?

While it is important to analyze who is being identified for housing support,
it is equally important to evaluate who is being missed. The statistics for
the transitional clients not flagged by RAPID are shown in Table 9. Consistent
with our understanding of transitional clients, as discussed in Section 3,
Table 9 shows a client population with a small number of total stays and
episodes. The shelter usage percentages are high, primarily due to the large
number of clients with a single stay which corresponds to a 100% shelter use
percentage (1 stay divided by 1 day).

The most significant item to highlight in Table 9 is the 90th percentile
tenure value. This group of clients, corresponding to 1289 individuals or 7.0%
of the total client population, has a period of shelter interaction of 1450 or
more days. As acknowledged in Section 4.1, these are not days of continual
interaction and likely contain large gaps where the client is absent from the
shelter system.

To explore this further, the clients in the 90th percentile of Table 9 are
analyzed as a separate cohort. Within this group, the average number of days
between episodes of shelter access is 635.8. This creates a picture of a
population who interact with an emergency shelter over a period of several
years with gaps in that interaction of longer than a year. These clients do
not use the shelter system intensively enough to be flagged as chronic or
episodic but obviously are existing for very long periods in precarious
circumstances. At 7.0% of the client population, the size of this cohort is
significant and is comparable to the number of clients that would be referred
to housing services by the government definitions in Table 8.

| Mean | Median | 90th Percentile
---|---|---|---
Total Stays | 14.9 | 2.0 | 40.0
Total Episodes | 1.6 | 1.0 | 3.0
Tenure (days) | 382.7 | 7.0 | 1450.0
Usage Percentage | 59.6% | 93.5% | 100.0%
Coverage: 12891/18398 (70.0%)
Table 9: Clients not identified by RAPID

##  7 Concluding Remarks

Identifying the cohort of people most in need of housing services as quickly
as possible is important. The primary contribution of this paper is to examine
how best to do this based on a client’s shelter access pattern. The stays
saved and tenure reduction metrics we develop are a new approach for
evaluating how well a test for chronic/episodic shelter access satisfies the
tradeoff between program efficiency and rapid identification of candidates.

Using these metrics, we present the RAPID tests that we believe are best for
identifying chronic/episodic shelter use. Our tests have the potential to
identify clients for housing support almost 200 days sooner than the next
fastest definition for chronic homelessness. The demographic results we
present demonstrate that, while fast, RAPID also selects the high impact group
of clients that are most in need of housing support.

In the process of evaluating our tests, we have also illustrated the dramatic
potential of Housing First services. Providing a housing intervention at the
point in time when a client is identified as a chronic/episodic shelter user
has the potential to save hundreds of shelter stays and, in some cases, over
1000 days of shelter interaction per referral.

While this study has been performed in a Canadian context, our results can be
generalized to other jurisdictions. As noted in Section 3, variation does
exist between homeless populations in different cities. Ideally, before RAPID
is used in a jurisdiction, its performance would ideally be evaluated on a
historical shelter dataset from that area. However, this is not a requirement.
The primary difference between RAPID and other chronic definitions is the
reduced time window and stay/episode threshold. While we believe that our
values will work for most cities, program administrators can always adjust
RAPID for their circumstances. For example, using RAPID in areas where even
transitional users have a large number of stays, like Philadelphia and
Massachusetts [6], may result in too many housing referrals. In these cases,
administrators could use RAPID as a starting point and increase the threshold
and time window parameters over time in order to manage program load.

Finally, we argue that it is worth taking a deeper look at the transitional
client population who are not flagged as chronic or episodic. While their
number of stays and episodes are low on average, our analysis demonstrates
that there is still a large percentage of the client population that interact
with emergency shelters “under the radar” for several years. Any individual
who interacts with an emergency shelter even on a very intermittent basis over
several years is not in a stable situation. To provide assistance to this
group, a good first step would be to flag clients on their very first return
visit to shelter after a long absence for referral to a counselor.

## References

  * [1] A. Afifi, S. May, V.. Clark and R. Donatello  “Practical Multivariate Analysis”  CRC Press, 2011
  * [2] T Aubry et al.  “Screening for housing first”  In _Canadian Observatory on Homelessness and the Mental Health Commission of Canada_ , 2015
  * [3] T. Aubry, S. Farrell, S. Hwang and M. Calhoun  “Identifying the patterns of emergency shelter stays of single individuals in Canadian cities of different sizes”  In _Housing Studies_ 28.6 Taylor & Francis, 2013, pp. 910–927
  * [4] T. Byrne and D.. Culhane  “Testing alternative definitions of chronic homelessness”  In _Psychiatric Services_ 66.9 Am Psychiatric Assoc, 2015, pp. 996–999
  * [5] Calgary Drop-In Centre  “More than Emergency Shelter: 2018-19 Report to Community”, 2019  URL: https://www.calgarydropin.ca/cms/wp-content/uploads/2019/11/Report-to-Community-final.pdf
  * [6] D.. Culhane et al.  “Testing a typology of family homelessness based on patterns of public shelter utilization in four US jurisdictions: Implications for policy and program planning”  In _Housing Policy Debate_ 18.1 Taylor & Francis, 2007, pp. 1–28
  * [7] Employment and Social Development Canada  “Reaching Home: Canada’s Homelessness Strategy Directives”, 2019  URL: https://www.canada.ca/en/employment-social-development/programs/homelessness/directives.html
  * [8] S. Gaetz, E. Dej, T. Richter and M. Redman  “The State of Homelessness in Canada 2016”  Toronto, Ontario, Canada: Canadian Observatory on Homelessness Press, 2016
  * [9] S. Gaetz, T. Gulliver and T. Richter  “The State of Homelessness in Canada 2014”  Toronto, Ontario, Canada: Canadian Homelessness Research Network, 2014
  * [10] P. Goering et al.  “National final report: Cross-site at home/chez soi project”  In _Mental Health Commission of Canada_ 48, 2014
  * [11] T. Hastie, R. Tibshirani and J. Friedman  “The Elements of Statistical Learning: Data Mining, Inference and Prediction”  Springer, 2017
  * [12] R.. Kneebone, M. Bell, N. Jackson and A. Jadidzadeh  “Who are the Homeless? Numbers, Trends and Characteristics of those without Homes in Calgary”  In _SPP Research Paper_ , 2015
  * [13] R. Kuhn and D.. Culhane  “Applying cluster analysis to test a typology of homelessness by pattern of shelter utilization: Results from the analysis of administrative data”  In _American journal of community psychology_ 26.2 Wiley Online Library, 1998, pp. 207–232
  * [14] G.. Milligan and M.. Cooper  “A study of standardization of variables in cluster analysis”  In _Journal of classification_ 5.2 Springer, 1988, pp. 181–204
  * [15] M. Shinn and R. Cohen  “Homelessness prevention: A review of the literature”  In _Center for Evidence-Based Solutions to Homelessness_ , 2019
  * [16] S.. Snyder et al.  “A Plan for Alberta: Ending Homelessness in 10 Years”, 2008


[table]capposition=top figuret

11institutetext:  Rapid-Rich Object Search (ROSE) Lab, Nanyang Technological
University 22institutetext: School of Electrical and Electronic Engineering,
Nanyang Technological University 33institutetext: College of Computer Science
and Technology, Zhejiang University 44institutetext: The State Key Lab of
Brain-Machine Intelligence, Zhejiang University
44email: {ZONGRUI001<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>††† Equal contribution. ✉ Corresponding author.

# Connecting Consistency Distillation to Score Distillation for Text-to-3D
Generation

Zongrui Li 112 †2 † 0009-0003-4357-9593 Minghui Hu 2 †2 † 0000-0002-3658-0890
Qian Zheng ✉ 3344 0000-0003-3968-3622 Xudong Jiang 22 0000-0002-9104-2315

###### Abstract

Although recent advancements in text-to-3D generation have significantly
improved generation quality, issues like limited level of detail and low
fidelity still persist, which requires further improvement. To understand the
essence of those issues, we thoroughly analyze current score distillation
methods by connecting theories of consistency distillation to score
distillation. Based on the insights acquired through analysis, we propose an
optimization framework, Guided Consistency Sampling (GCS), integrated with 3D
Gaussian Splatting (3DGS) to alleviate those issues. Additionally, we have
observed the persistent oversaturation in the rendered views of generated 3D
assets. From experiments, we find that it is caused by unwanted accumulated
brightness in 3DGS during optimization. To mitigate this issue, we introduce a
Brightness-Equalized Generation (BEG) scheme in 3DGS rendering. Experimental
results demonstrate that our approach generates 3D assets with more details
and higher fidelity than state-of-the-art methods. The codes are released at
https://github.com/LMozart/ECCV2024-GCS-BEG.

###### Keywords:

Text-to-3D Generation Score Distillation Sampling Consistency Model

##  1 Introduction

Text-to-3D generation [17, 29, 43, 44, 4, 11, 27] has gained substantial
attention due to its great potential and indispensable role in many
applications, such as gaming, filmmaking, and architecture. While an end-to-
end text-to-3D generative model [11, 27] is often difficult to train and lacks
versatility due to the limited 3D assets in the training set, distillation 3D
assets from a well-trained 2D generative model (_e.g._ , diffusion model (DM)
[9, 30]) has become a popular option due to its data-free feature. A typical
work, DreamFusion [29], transfers knowledge from the pre-trained diffusion
model to a learnable 3D representation through Score Distillation Sampling
(SDS), generating text-aligned 3D assets.

Nevertheless, as highlighted in many subsequent works [43, 44, 17, 45, 39],
SDS suffers from a low level of detail in generation results. Such an issue
stems from the poor generalization ability of the distillation method [43] and
the inherent randomness in the sampling process [17, 44]. Although work like
[43] is proposed to enhance the generalization ability, it necessitates fine-
tuning the diffusion model during training, dramatically extending the
training time. By contrast, more recent works [44, 17] aim to mitigate the
randomness in the sampling process by introducing Probability Flow Ordinary
Differential Equations (PF-ODEs) [38], and speed up the distillation process
through 3D Gaussian Splatting (3DGS) [13], resulting in cost-efficient, high-
quality 3D generation.

Figure 1: Text-to-3D generation results of the proposed Guided Consistency
Sampling (GCS) and Brightness-equalized Generation. Each 3D asset is distilled
from a pre-trained 2D diffusion model and demonstrated with three different
views. The results below the dotted line are generated by the fine-tuned
diffusion models.

Despite the effectiveness of score distillation methods, issues like limited
detail and low fidelity remain in the generated 3D asset. To reveal the
essence of those issues, we conduct an in-depth analysis to connect
consistency distillation [37, 14, 51], a method that distills information from
a pre-trained DM through PF-ODEs, to score distillation. Such a novel view
helps us identify potential causes of those issues in the score distillation
process: 1) the inherent distillation errors of PF-ODEs, 2) ineffective
conditional guidance accounting for classifier-free guidance (CFG) effects
[10], and 3) lack of constraints in pixel domain to avoid out-of-distribution
problem, requiring further improvements.

Except for identified issues in score distillation, there is another
noteworthy concern in the 3D rendering process, _i.e_ , the over-saturated
views for generated 3D asset [43, 17, 44]. While the cause of such an issue is
correlated with types of 3D representation, this paper particularly focuses on
one (_i.e_ , 3DGS) due to its remarkable reduction in optimization time.
Through experiments, we observe that the brightness in generated 2D views
accumulates to the next epoch during distillation, eventually leading to over-
saturation.

To achieve better performance and overcome the aforementioned issues, this
paper proposes Guided Consistency Sampling (GCS) with Brightness-equalized
Generation (BEG) for 3DGS-based text-to-3D generation (Fig. 2). The proposed
GCS includes three components to solve the identified issues in score
distillation: a compact consistency loss reduces distillation errors, a
conditional guidance loss provides more effective conditional guidance, and a
constraint on pixel domain enhances the fidelity of the 3D assets.
Additionally, the proposed BEG helps regularize the accumulation of brightness
in 3DGS, which significantly alleviates over-saturation issues. Examples of
generated 3D assets can be found in Fig. 1. In summary, our contributions are
as follows:

  1. 1.

We identify three problems in the PF-ODEs-based score distillation method by
connecting consistency distillation to score distillation.

  2. 2.

We propose Guided Consistency Sampling, an improved score distillation method,
to enhance the details and fidelity of the generated 3D asset.

  3. 3.

We find an accumulated brightness issue in the 3DGS-based rendering process
that causes over-saturation and propose Brightness-equalized Generation to
alleviate it in the 3DGS-based rendering process.

Figure 2: An overview of the proposed GCS. We first initialize the 3D
representation via the pre-trained 3D generator. For each training epoch, we
randomly render a batch of views $\mathbf{x}_{\pi}$ and diffuse them to
$\mathbf{x}_{\\{\pi,e\\}}$ with a fixed noise $\epsilon^{*}$. We then apply
the ODE diffusion process to gradually add noise to the
$\mathbf{x}_{\\{\pi,e\\}}$ and transfer it to
$\bar{\mathbf{x}}_{\\{\pi,e\rightarrow s\\}}$ and
$\bar{\mathbf{x}}_{\\{\pi,s\rightarrow t\\}}$. In the denoising path, we
conduct conditional and unconditional denoising steps, as shown in the figure.
Eventually, we calculate the $\mathcal{L}_{\text{GCS}}$ (Eq. 17) to update the
parameters of 3D representation (3DGS). Note that we add ‘$*$’ on
$\bar{\mathbf{x}}_{\\{\pi,e\rightarrow 0;y\\}}$ to indicate that it is
obtained from different sampling trajectories.

##  2 Related Work

Text-to-3D Generation by Score Distillation. SDS, introduced in DreamFusion
[29], and concurrent Score Jacobian Chain (SJC) proposed in [42], have been
regarded as milestone works in distilling information from a 2D pre-trained
diffusion models to differentiable 3D representations, which inspiring many
subsequent Text-to-3D generation methods [33, 4, 18, 7, 43, 53, 5, 44, 40, 39,
24, 41, 12, 35, 48, 19, 49, 47] to improve the quality of generated 3D assets.
Generally, they either endow the DM with the pose-aware generative ability
[24, 19, 49, 35, 48, 41] to alleviate the Janus problem [1] for a more
consistent 3D asset, or redesign the distillation process and optimization
objectives [4, 18, 53, 43, 47, 12, 44, 5] to reduce the distillation error
from the 2D pre-trained diffusion model for a higher level of details. While
the performance of the former methods may be restricted by the inherent
limitations of SDS [17], the latter methods dedicated to overcoming these
limitations have recently gained increasing attention. For instance,
ProlificDreamer [43] proposes sampling from the parameter distribution instead
of seeking the optimal solution for high-fidelity generation. CSD [10]
introduces insights into the effects of SDS’s components and proposes improved
strategies. More recent works like [17, 44] introduce PF-ODEs into the SDS for
a stable, deterministic distillation process. After thoroughly investigating
recent works, we recognize a connection between consistency distillation and
score distillation, which motivates us to analyze and redesign the
optimization objectives in view of consistency distillation. Although
concurrent work [44] also highlighted the effectiveness of text-to-3D
generation using consistency distillation, our analysis delves deeper into
such connection from a broader perspective. We also compare with the findings
of [44] in Tab. 1. Another concurrent study [23] established a relationship
between SDS and bridge matching [6, 15], leading to an improvement similar to
that seen in our method. Guided by acquired insights, we propose GCS that
integrates techniques in CM to improve generation quality and gain state-of-
the-art performance.

Differentiable 3D Representations, such as NeRF [43, 17, 29, 25], 3DGS [13,
39, 7], or learnable intrinsic that integrated with differentiable geometry
[4, 34] and textures [3, 16, 8, 2], can be optimized by minimizing the loss
between rendered and ground truth images, establishing a connection between 3D
and 2D representations. Text-to-3D by distillation relies heavily on
differentiable 3D representations. While NeRF is well-known to be slow to
optimize, we use 3DGS considering its efficiency and comparable performance
with NeRF.

##  3 Preliminary

Diffusion Models (DM) [9, 31] apply a forward process to perturb data samples
$\mathbf{x}_{0}$ drawn from a data distribution $p_{\text{data}}(\mathbf{x})$
by the Gaussian noise $\mathcal{N}(\mathbf{0},\sigma^{2}_{t}\mathbf{I})$ with
time-dependent variance $\sigma_{t}$, where $t\in[0,T]$. As such, the
distribution of noisy samples $\mathbf{x}_{t}$ at time-step $t$ is:

$\displaystyle
p_{t}\left(\mathbf{x}_{t}\mid\mathbf{x}_{0}\right)=\mathcal{N}\left(\mathbf{x}_{t};\mathbf{x}_{0},\sigma_{t}^{2}\mathbf{I}\right),$
(1)

which can be re-parameterized to
$\mathbf{x}_{t}=\alpha_{t}\mathbf{x}_{0}+\sigma_{t}\bm{\epsilon}_{t}$, where
$\epsilon_{t}\sim\mathcal{N}(\mathbf{0},\mathbf{I})$. A reverse process can
denoise the noisy samples from $\mathbf{x}_{t}$ to $\mathbf{x}_{0}$, expressed
as variational inference of Markov processes [9]. For all diffusion processes,
there exists a corresponding deterministic process with trajectory sharing the
same marginal distribution, known as PF-ODE [38]:

$\text{\it PF-ODE: }\
\mathrm{d}\mathbf{x}_{t}=\left[\mathbf{f}(\mathbf{x}_{t},t)-\frac{1}{2}g(t)^{2}\nabla_{\mathbf{x}_{t}}\log
p_{t}(\mathbf{x}_{t})\right]\mathrm{d}t,$ (2)

where $\mathbf{f}(\mathbf{x}_{t},t)$ is the drift coefficients, $\mathrm{d}t$
is the infinitesimal negative timestep, $\nabla_{\mathbf{x}_{t}}\log
p_{t}(\mathbf{x}_{t})$ is the score function of $p_{t}(\mathbf{x}_{t})$,
estimated by a neural network
$\bm{\epsilon}_{\theta}\left(\mathbf{x}_{t},t\right)$. An ODE solver (_e.g._ ,
DDIM [36], DPM-Solver [20], etc.) can be used to derive the solution of ODE,
identical as a sampling process. The sampling trajectory of ODE is
deterministic, and the randomness comes from the initial value, which is more
stable than a random sampling process described by the inverse Stochastic
Differentiable Equation (SDE) [38].

Consistency Model (CM) [37] is proposed to facilitate a single-step or low
number of function evaluations (NFEs) [28] generation by distilling knowledge
from pre-trained DM models. It defines a one-step generator
$\bm{f}_{\theta}(.;.)$ with trainable parameters $\theta$ that directly
predicts the denoised image $\mathbf{x}_{0}$ given $t$ and $\mathbf{x}_{t}$,
constrained by some boundary conditions [37]. $\bm{f}_{\theta}(.;.)$ is
trained by minimizing consistency distillation loss [37] defined as:

$\displaystyle\mathcal{L}_{\mathrm{CD}}\left(\bm{\theta},\bm{\theta}^{-}\right)=\quad\mathbb{E}\left[\omega(t)\left\|\bm{f}_{\bm{\theta}}\left(\mathbf{x}_{t_{n+1}};t_{n+1}\right)-\bm{f}_{\bm{\theta}^{-}}\left(\bar{\mathbf{x}}_{\\{t_{n+1}\rightarrow
t_{n}\\}};t_{n}\right)\right\|_{2}^{2}\right],$ (3)

where, $0=t_{1}<t_{2}\cdots<t_{N}=T$, $\bar{\mathbf{x}}_{\\{t_{n+1}\rightarrow
t_{n}\\}}$ is calculated given ODE solver $\Phi(.)$ as
$\bar{\mathbf{x}}_{\\{t_{n+1}\rightarrow
t_{n}\\}}=\Phi\left(\mathbf{x}_{t_{n+1}};t_{n+1},t_{n}\right)$,
$\bm{\theta}^{-}$ is updated during training process through an exponential
moving average (EMA) strategy [38]. The ultimate goal of CM is to maintain the
self-consistency condition along the trajectory
$\\{\mathbf{x}_{t}\\}_{t\in[0,T]}$, satisfying,

$\displaystyle\bm{f}\left(\mathbf{x}_{t};t\right)=\bm{f}\left(\mathbf{x}_{t^{\prime}};t^{\prime}\right)\quad\forall
t,t^{\prime}\in[0,T].$ (4)

Subsequent works of CM [10, 51, 14] integrate Classifier-free guidance (CFG)
[10] or jumps along PF-ODE trajectory into the CM for high-fidelity samples
given low or high NFEs, respectively. Inspired by those works, we seek to
improve the performance of SDS further in view of CM given their connection.

##  4 Methodology

In Sec. 4.1, we analyze current advances [29, 47, 43, 17, 44] in a unified
framework obtained by connecting consistency distillation [14, 51, 37] to
score distillation. We revisited and identified three problems in the current
PF-ODEs-based score distillation from the perspective of consistency
distillation. We further proposed our solution, _i.e_., Guided Consistency
Sampling (GCS), and explained in detail in Sec. 4.2. While GCS is integrated
with 3DGS, we observe the accumulated brightness causing over-saturation in
3DGS, as explained in Sec. 4.3. We propose Brightness Equalized Generation
(BEG) to alleviate this issue.

###  4.1 Connecting Consistency Distillation to Score Distillation

Table 1: Specific design space employed by proposed GCS and selected 2D
diffusion-based score distillation text-to-3D generation method.

|  DreamFusion [29] |  ProlificDreamer [43] |  Consistent3D [44]
---|---|---|---
3D Representation | NeRF / GS | NeRF | NeRF / GS
CFG Weight | - | 7.5+ | 50+
Objective | SDS (Eq. 7) | VSD (Eq. 9) | CDS (Eq. 15)
Objective #1: Generator Loss |  |  |
term A | $\mathbf{x}_{\pi}$ | $F_{\phi}\left(\mathbf{x}_{\\{\pi,t\\}};t,y\right)$ | $F_{\theta}\left(\mathbf{x}_{\\{\pi,t\\}};t,y\right)$
term B | $F_{\theta}\left(\mathbf{x}_{\\{\pi,t\\}};t,y\right)$ | $F_{\theta}\left(\mathbf{x}_{\\{\pi,t\\}};t,y\right)$ | $F_{\theta}\left(\bar{\mathbf{x}}_{\\{\pi,t\rightarrow s;y\\}};s,y\right)$
|  LucidDreamer [17] |  DreamFusion w/ CFG [29] | Ours
3D Representation | NeRF / GS | NeRF / GS | GS w/ BEG
CFG Weight | 7.5+ | 100+ | 7.5+
Objective | ISD (Eq. 13) | SDS w/ CFG (Eq. 4.1) | GCS (Eqs. 20, 22, 23)
Objective #1: Generator Loss |  |  |
term A | - | $\mathbf{x}_{\pi}$ | $G_{\theta}\left(\hat{\mathbf{x}}_{\\{\pi,t\\}};t,e,\emptyset\right)$
term B | - | $F_{\theta}\left(\mathbf{x}_{\\{\pi,t\\}};t,y\right)$ | $F_{\theta}\left(\bar{\mathbf{x}}_{\\{\pi,t\rightarrow s;y\\}};s,e,\emptyset\right)$
Objective #2: Classifier Loss |  |  |
term A | $F_{\theta}\left(\hat{\mathbf{x}}_{\\{\pi,s\\}};s,\emptyset\right)$ | $F_{\theta}\left(\mathbf{x}_{\\{\pi,t\\}};t,\emptyset\right)$ | $F_{\theta}\left(\hat{\mathbf{x}}_{\\{\pi,e\\}};e,\emptyset\right)$
term B | $F_{\theta}\left(\hat{\mathbf{x}}_{\\{\pi,t\\}};t,y\right)$ | $F_{\theta}\left(\mathbf{x}_{\\{\pi,t\\}};t,y\right)$ | $F_{\theta}\left(G_{\theta}\left(\hat{\mathbf{x}}_{\\{\pi,t\\}};t,e,y\right);e,y\right)$
Pixel Constraint |  |  $+$SDS on pixel domain [53] |  $+\mathcal{L}_{\mathrm{CP}}$ (Eq. 23)

Through theoretical analysis, we find that consistency and score distillation
share a similar optimization objective. While CM enforces a self-consistency
of a PF-ODE sampling trajectory (Eq. 3), SDS and its variants (score
distillation) facilitate a cross-consistency111We define cross-consistency as
an alignment between the diffusion trajectory of the rendered view and the
text-conditioned sampling trajectory. between the diffusion trajectory of the
rendered view and the denoising trajectory (usually with text condition) of a
noisy sample. This cross-consistency is maintained by minimizing the gap
between a sample on the diffusion and denoising trajectory. The score
distillation method diversifies in choosing those samples to form the
optimization objectives (see Tab. 1 for a summary). In the following part, we
unify the optimization objective of the score distillation method by sample
(${\mathbf{x}}$) instead of score ($\epsilon$) to connect consistency
distillation to score distillation based on their similarity.

In vanilla SDS, given a camera poses $\pi$, a 3D representation $\xi$ can be
projected to a specific 2D view, noted as $\mathbf{x}_{\pi}=g(\pi,\xi)$. The
optimization objective of SDS on 3D parameters $\xi$ is given as:

$\displaystyle\min_{\xi}\mathcal{L}_{\mathrm{SDS}}(\xi)=\mathbb{E}_{t,\pi}\left[\omega(t)\left\|\bm{\epsilon}_{\theta}\left(\mathbf{x}_{t};t,y\right)-\bm{\epsilon}\right\|^{2}_{2}\right],$
(5)

where $\epsilon_{\theta}\left(\mathbf{x}_{t};t,y\right)$ is the predicted
noise given $\mathbf{x}_{t}$, time-step $t$, and $y$; $\omega(t)$ is a $t$
related weight function. As suggested in [52, 53, 32], SDS loss is equivalent
to:

$\displaystyle\mathcal{L}_{\mathrm{SDS}}(\xi)$
$\displaystyle=\mathbb{E}_{t,\pi}\left[\omega(t)\left\|\bm{\epsilon}_{\theta}\left(\mathbf{x}_{\\{\pi,t\\}};t,y\right)-\bm{\epsilon}\right\|^{2}_{2}\right],$
(6)
$\displaystyle=\mathbb{E}_{t,\pi}\left[c(t)\left\|\mathbf{x}_{\\{\pi,t\\}}-F_{\theta}(\mathbf{x}_{\\{\pi,t\\}};t,y)\right\|_{2}^{2}\right],$
(7) $\displaystyle=:\mathcal{L}_{\text{Distill}}(\xi),$ (8)

where
$\mathbf{x}_{\\{\pi,t\\}}=\alpha_{t}\mathbf{x}_{\pi}+\sigma_{t}\epsilon$,
$F_{\theta}(\mathbf{x}_{\\{\pi,t\\}};t,y)=\frac{\mathbf{x}_{\\{\pi,t\\}}-\sigma_{t}\bm{\epsilon}_{\theta}\left(\mathbf{x}_{\\{\pi,t\\}};t,y\right)}{\alpha_{t}}$,
$c(t)$ is another $t$ related weight function. In CM [22, 9],
$\bm{f}_{\theta}(.;.)$ can be parameterize as $F_{\theta}(.;.)$, which makes
Eq. 3 similar to Eq. 7 in formula. As stated in [36, 44], we interpret
minimizing $\mathcal{L}_{\text{SDS}}$ as facilitating a cross-consistency of
the stochastic and deterministic trajectory. The variance of SDS injects
different conditions on samples. For instance, replacing $\mathbf{x}_{\pi}$ by
samples from another fine-tuning diffusion model, noted as
$F_{\phi}(\mathbf{x}_{\\{\pi,t\\}};t,y)$ in Eq. 7, we have Variational Score
Distillation (VSD) [43] as:

$\mathcal{L}_{\text{VSD}}(\xi)=\mathbb{E}_{t,\pi}\left[c(t)\left\|F_{\phi}(\mathbf{x}_{\\{\pi,t\\}};t,y)-F_{\theta}(\mathbf{x}_{\\{\pi,t\\}};t,y)\right\|_{2}^{2}\right],$
(9)

which distills information by enforcing cross-consistency of the trajectory
parameterized by $\phi$ and $\theta$. In practice, CFG with a higher guidance
weight $w$ (_e.g._ , $w=100$) is imperative in SDS. Specifically, the
expression of SDS with CFG in the form of distillation loss [10, 47] is:

$\displaystyle\mathcal{L}^{\text{CFG}}_{\text{Distill}}(\xi):=\mathbb{E}_{t,\pi}[c(t)\|$
$\displaystyle\underbrace{[\mathbf{x}_{\pi}-F_{\theta}(\mathbf{x}_{\\{\pi,t\\}};t,y)]}_{\text{generator
loss}}$ $\displaystyle+$ $\displaystyle
w\underbrace{[F_{\theta}(\mathbf{x}_{\\{\pi,t\\}};t,\emptyset)-F_{\theta}(\mathbf{x}_{\\{\pi,t\\}};t,y)]}_{\text{classifier
loss}}\|_{2}^{2}].$ (10)

Notably, we extend the definition in [47], noting the generator loss as a
guidance to make ${\mathbf{x}}_{\pi}$ more close to the prior distribution and
the classifier loss as an update direction for ${\mathbf{x}}_{\pi}$ to align
with the text-condition. As studied in [47], the driving force of SDS is the
classifier loss. By omitting the generator loss, they derive Classifier Score
Distillation (CSD), given:

$\displaystyle\mathcal{L}_{\text{CSD}}(\xi):=\mathbb{E}_{t,\pi}[c(t)\|[F_{\theta}(\mathbf{x}_{\\{\pi,t\\}};t,\emptyset)-F_{\theta}(\mathbf{x}_{\\{\pi,t\\}};t,y)]\|_{2}^{2}].$
(11)

Additionally, as shown in [17], $\mathbf{x}_{\\{\pi,t\\}}$ could be replaced
by the deterministic status derived from DDIM to improve the distillation
quality:

$\hat{\mathbf{x}}_{\\{\pi,t\\}}=\sum^{s}_{k=0}\alpha_{(k+\delta_{k})}\left(\frac{1}{\alpha_{k}}\mathbf{x}_{k}-\frac{\sigma_{(k+\delta_{k})}}{\alpha_{(k+\delta_{k})}}\epsilon_{\theta}(\mathbf{x}_{k};k,\emptyset)\right)+\sigma_{(k+\delta_{k})}\epsilon_{\theta}(\mathbf{x}_{k};k,\emptyset),$
(12)

where $t>s$ with $t=s+\delta_{s}$. Similar to derive Eq. 8, based on Eq. 12,
we can express Interval Score Distillation (ISD) [17] as follows:

$\mathcal{L}_{\text{ISD}}(\xi)=\mathbb{E}_{t,s,\pi}\left[c(t)\left\|F_{\theta}(\hat{\mathbf{x}}_{\\{\pi,s\\}};s,\emptyset)-F_{\theta}(\hat{\mathbf{x}}_{\\{\pi,t\\}};t,y)\right\|_{2}^{2}\right],$
(13)

which can be regarded as a classifier loss. With CFG, an additional generator
loss is combined with ISD,

$\displaystyle\begin{aligned}
\mathcal{L}^{\text{CFG}}_{\text{ISD}}(\xi)=\mathbb{E}_{t,s,\pi}[c(t)&\|[F_{\theta}(\hat{\mathbf{x}}_{\\{\pi,s\\}};s,\emptyset)-F_{\theta}(\hat{\mathbf{x}}_{\\{\pi,t\\}};t,\emptyset)]\\\
&+w[F_{\theta}(\hat{\mathbf{x}}_{\\{\pi,t\\}};t,\emptyset)-F_{\theta}(\hat{\mathbf{x}}_{\\{\pi,t\\}};t,y)],\|^{2}_{2}],\end{aligned}$
(14)

we find the generator loss in Eq. 14 is highly correlated to a Consistency
Distillation Sampling (CDS) studied in [44]:

$\displaystyle\mathcal{L}_{\text{CDS}}(\xi)=\mathbb{E}_{t,s,\pi}\left[c(t)\|F_{\theta}(\mathbf{x}_{\\{\pi,t\\}};t,y)-F_{\theta}(\bar{\mathbf{x}}_{\\{\pi,t\rightarrow
s;y\\}};s,y)\|^{2}_{2}\right],$ (15)

where, $\bar{\mathbf{x}}_{\\{\pi,t\rightarrow
s;y\\}}=F_{\theta}\left(\mathbf{x}_{\\{\pi,t\\}};t,s,y\right)=\Phi\left(\mathbf{x}_{\\{\pi,t\\}};t,s,y\right)$.
Particularly, CDS is a special case as it mainly guides the generated views to
match a particular origin of PF-ODE trajectory from the prior distribution
through self-consistency. In such case, an upper bound for the distillation
error can be deduced [44]:

$\displaystyle\left\|\mathbf{x}_{\pi}-\mathbf{x}_{0}\right\|_{2}=\mathcal{O}\left((\Delta
t)^{p}\right)T.$ (16)

where $\mathbf{x}_{0}\sim p_{\text{data}}(\mathbf{x})$ is an real image,
$\Delta t=\max\left\\{\left|\delta_{k}\right|\right\\}$, $k\in[0,...,s]$ and
$t=s+\delta_{s}$. With CFG, CDS can further facilitate a cross-consistency of
text and null condition trajectories. However, it performs poorly with low CFG
weight [44], which needs further improvement. Inspired by the similarity of CM
and the optimization objectives of the score distillation method, we are
motivated to reformulate the optimization objective in SDS by extending the
theories in CM to improve text-to-3D generation quality. We sum up our
solution in three aspects: 1) we reduce the error bound suggested Eq. 16 to
improve the distillation quality; 2) we provide more reliable guidance during
distillation accounting for CFG effects; 3) we implement constraints on pixel
domain to enhance the fidelity.

###  4.2 Guided Consistency Sampling

In this section, we introduce the Guided Consistency Sampling (GCS), which
includes three parts of objectives: a Compact Consistency (CC) loss, a
Conditional Guidance (CG) score, and a Constraint on Pixel domain (CP):

$\mathcal{L}_{\text{GCS}}(\xi)=\mathcal{L}_{\text{CC}}(\xi)+\mathcal{L}_{\text{CG}}(\xi)+\mathcal{L}_{\text{CP}}(\xi).$
(17)

Compact Consistency (CC) Loss aims to improve further the self-consistency of
PF-ODE denoising trajectory, which eventually reduces the distillation error
bound in Eq. 16 for a more aligned distribution of rendered views. Inspired by
[14, 51], we define a solution function:

$G_{\theta}({\mathbf{x}}_{t};t,s,y):={\mathbf{x}}_{t}+\int_{t}^{s}\frac{{\mathbf{x}}_{u}-\mathbb{E}[{\mathbf{x}}|{\mathbf{x}}_{u}]}{u}\text{d}u.$
(18)

which $G_{\theta}({\mathbf{x}}_{t};t,s,y)$ solves the PF-ODE from initial time
$t$ to a final time $s$ according to exponential integrator [20, 21, 50].
Owing to the fact that $G$ is intractable as it can only be obtained by
calculating $s$ partial derivative at time $t$, we follow the scheme in [51]
and adhere to the first-order definition222For the effect of higher orders,
please refer to the Appendix for more details. of DPM-Solver [20], re-
parameterised $G$ as:

$G_{\theta}({\mathbf{x}}_{t};t,s,y)=\frac{\sigma_{s}}{\sigma_{t}}{\mathbf{x}}_{t}-\alpha_{s}(e^{-h}-1){\epsilon}_{\bm{\theta}}({\mathbf{x}}_{t},t,y),$
(19)

where $h=\lambda_{s}-\lambda_{t}$ with the $\log$-SNR $\lambda$ defined as
$\lambda=\log(\alpha/\sigma)$ and ${\epsilon}_{\bm{\theta}}$ is the prediction
from the network. According to the previous definition, we mathematically
define Compact Consistency Loss, a critical part of GCS, to improve the
details of the 3D asset:

$\mathcal{L}_{\text{CC}}(\xi)=\mathbb{E}_{t,s,e,\pi}\left[\|G_{\theta}(\hat{\mathbf{x}}_{\\{\pi,t\\}};t,e,\emptyset)-G_{\theta}(\bar{\mathbf{x}}_{\\{\pi,t\rightarrow
s;y\\}};s,e,\emptyset)\|^{2}_{2}\right],$ (20)

where $t>s>e$, and $\hat{\mathbf{x}}_{\\{\pi,t\\}}$ is obtained by DDIM
inversion from ${{\mathbf{x}}}_{\\{\pi,e\\}}$, calculated as
${{\mathbf{x}}}_{\\{\pi,e\\}}=\alpha_{e}{\mathbf{x}}_{\pi}+\sigma_{e}\epsilon^{*}$
to $\bar{{\mathbf{x}}}_{\\{\pi,e\rightarrow s\\}}$ and eventually to
$\bar{{\mathbf{x}}}_{\\{\pi,s\rightarrow t\\}}$. A null condition is applied
to all DDIM inversion steps. Notably, $\epsilon^{*}$ is the random noise that
will only be sampled once and kept fixed in practice333We use $\epsilon^{*}$
to ensure a valid diffusion process at low time step and reduce the
computational cost, compared to [17].. During the training process, the
parameters in the pre-trained model are frozen. In this condition, we
substantiated Lemma 1, which extends the premises established in [44, 37].

######  Lemma 1 ([51, 37, 14, 44])

Let $\Delta t=\max\left\\{\left|\delta_{k}\right|\right\\}$,
$k\in[0,...,n_{s}]$, where $n_{s}$ is the index of $\delta$ at time step $s$,
and $F_{\theta}(\cdot,\cdot)$ is the origin prediction function grounded on
the empirical PF-ODE. Assume $F_{\theta}$ satisfies the Lipschitz condition,
if there is a ${\mathbf{x}}_{\pi}$ satisfying $\mathcal{L}_{\rm{CC}}(\xi)=0$,
given an image ${\mathbf{x}}_{0}\sim p_{\text{data}}({\mathbf{x}})$, for any
$t,s,e\in[\\![0,...,T]\\!]$ with $t>s>e$, we have:

$\begin{split}\mathop{\textnormal{sup}}\limits_{t,e,{\mathbf{x}}_{\pi}}\|\hat{{\mathbf{x}}}_{\\{\pi,e\\}},\hat{{\mathbf{x}}}_{\\{0,e\\}}\|_{2}=\mathcal{O}\left((\Delta
t)^{p}\right)(T-e),\end{split}$ (21)

$\hat{{\mathbf{x}}}_{\\{0,e\\}}$ is the distribution of ${\mathbf{x}}_{0}$
diffused to time $e$, $p$ is the order of ODE solver.

###### Proof

The proof is provided in the Appendix for completeness.

Lemma. 1 validates that CC achieves a lower upper limit on error margins than
CDS (Eq. 16) for a better distillation from the pre-trained model. Considering
the importance of CFG in generating high-quality contents, another issue worth
noting is whether it is practical to integrate CFG (or Perp-Neg [1]) into a
generator loss $\mathcal{L}_{\text{CC}}$. In CDS, it applies CFG in every ODE
denoising step, which leads to a large accumulated error magnified by CFG [22,
26]. Instead, we only implement CFG in one step [22] (see Fig. 2), leading to
lower accumulated errors. This strategy significantly improves the generation
quality with low CFG weight (see Fig. 3). However, we still observe artifacts
in the generated 3D model, likely due to a lack of effective classifier loss
that provides text-conditional guidance.

[capbesideposition=right,top]figure[]

Figure 3: Generated views by using $\mathcal{L}_{\text{CC}}$ with different
CFG strategies at a low CFG weight ($w=7.5$). While $\mathcal{L}_{\text{CC}}$
(left) implements CFG in only one denoising step,
$\mathcal{L}^{*}_{\text{CC}}$ (right) applies CFG in every ODE denoising step.

####  4.2.1 Conditional Guidance (CG) Loss

is proposed to accommodate guidance while maintaining a lower accumulated
error, which we interpret as conditional guidance. Inspired by [17, 26, 10],
we facilitate an alignment between the unconditional trajectory
($\mathcal{T}_{\\{e\rightarrow 0,\emptyset\\}}$ from a noisy sample at $e$ to
$0$) and the text-conditional trajectory ($\mathcal{T}_{\\{t\rightarrow
e\rightarrow 0,y\\}}$ derived from a noisy sample
$\hat{{\mathbf{x}}}_{\\{\pi,t\\}}$ then sampling down to $e$ and $0$),
separately. Mathematically, the CG score can be expressed as:

$\mathcal{L}_{\text{CG}}(\xi)=\mathbb{E}_{t,e,\pi}\left[\|F_{\theta}(\hat{\mathbf{x}}_{\\{\pi,e\\}};e,\emptyset)-F_{\theta}(G_{\theta}(\hat{\mathbf{x}}_{\\{\pi,t\\}};t,e,y);e,y)\|^{2}_{2}\right],$
(22)

where $F_{\theta}({\mathbf{x}};t,y)$ predicts the ${\mathbf{x}}_{0}$ from time
step $t$ given the conditional information $y$ as shown in Eq. 8, and
$G_{\theta}({\mathbf{x}};t,e,y)$ access the midpoint $e$ of the trajectory
from initial timestep $t$ as explained in Eq. 19. In practice, we can
integrate CFG into $\mathcal{L}_{\text{CG}}$ for better performance. We
believe the proposed $\mathcal{L}_{\text{CG}}$ provides more reliable guidance
with less accumulated error, as it avoids long navigation along the
trajectory. Specifically, the gap between $\mathcal{T}_{\\{e\rightarrow
0,\emptyset\\}}$ and $\mathcal{T}_{\\{t\rightarrow e\rightarrow 0,y\\}}$ is a
more precise guidance since it directly affects
$\hat{{\mathbf{x}}}_{\\{\pi,e\\}}$, which is a more similar sample to
${\mathbf{x}}_{\pi}$ [26] due to the DDIM inversion.

It is also interesting to see that $\mathcal{L}_{\text{ISD}}$ is equivalent to
$\mathcal{L}_{\text{CG}}$ when set $e=0$ in computing
$F_{\theta}(G_{\theta}(\hat{\mathbf{x}}_{\\{\pi,t\\}};t,e,y);e,y)$. We
intuitively explain the effect of a midpoint $e$ to reduce the error of one-
step denoising from a noisy sample conditioned at large $t$. Eventually, we
find $\mathcal{L}_{\text{CC}}$ and $\mathcal{L}_{\text{CG}}$ work together
improving the quality of generated 3D asset.

####  4.2.2 Constraint on Pixel (CP) Domain

aims to achieve a closer resemblance in the pixel domain for
$\mathcal{L}_{\text{CG}}$. While a satisfactory ${\mathbf{x}}_{\pi}$ is
obtained in the latent domain, whether such an ${\mathbf{x}}_{\pi}$ is equally
satisfactory in the pixel domain appears to have been overlooked. In fact, the
optimized ${\mathbf{x}}_{\pi}$ may not adhere to the prior distribution
stipulations of VAE, leading to out-of-distribution artifacts. Consequently,
this leads to unrealistic color in the decoded images (_e.g._ , a paint-like
color in the generated results of LucidDreamer [17]). Inspired by similar
methods proposed in [53], we further calculate $\mathcal{L}_{\text{CG}}$ in
the pixel domain for enhanced supervision. In this context, given an image
decoder $\mathcal{D}$ along with $\hat{\mathbf{x}}_{\\{\pi,e\\}}$, the
definition of CP can be articulated as follows:

$\displaystyle\mathcal{L}_{\text{CP}}(\xi)=\mathbb{E}_{t,e,\pi}\left[\|\mathcal{D}(\dot{{\mathbf{x}}}_{\pi})-\mathcal{D}(\tilde{{\mathbf{x}}}_{\pi})\|^{2}_{2}\right],$
(23)
$\displaystyle\dot{{\mathbf{x}}}_{\pi}=F_{\theta}(G_{\theta}(\hat{\mathbf{x}}_{\\{\pi,t\\}};t,e,y);e,y),$
(24)
$\displaystyle\tilde{{\mathbf{x}}}_{\pi}=F_{\theta}(\hat{\mathbf{x}}_{\\{\pi,e\\}};e,\emptyset).$
(25)

Our empirical observations indicate that optimizing CP yields notable
enhancements in color fidelity, albeit with increased computational cost and
over-saturation. Consequently, we suggest an additional strategy outlined in
Sec. 4.3, aimed at alleviating over-saturation. Extensive experiments lead us
to conclude that the CP term is constructive in bolstering the overall quality
of 3D assets.

###  4.3 Brightness-equalized Generation

A common problem in previous works is that the generated 3D assets often
suffer from over-saturation, especially in those that use Gaussian Splatting
as the 3D representation to be trained. We experimentally find that the high
brightness region (highlight) generated in the current training epoch is
carried over to the next epoch444A visualization of the brightness
accumulation can be found in the Appendix.. That is, the brightness of the
highlight points accumulates during training, eventually leading to over-
saturation. To alleviate this issue, we propose resetting the brightness of
the Gaussian555We use the average of RGB channels as the brightness.
adaptively according to the exposure status of the generated view.
Specifically, in each training epoch, we calculate the $m^{\mathrm{th}}$(85)
percentile of each image $\mathbf{x}^{i}_{\pi}$ in an image batch
$\mathbf{X}_{\pi}=\\{\mathbf{x}^{i}_{\pi},i\in[1,...,B]\\}$, noted as
$P_{m}=\\{p^{i}_{m},i\in[1,...,B]\\}$, where $B$ is the batch size. We then
find the maximum value in $P_{m}$ and reset the brightness of Gaussian to
$T_{\text{B}}=0.8$ of the current brightness if
$\operatorname{max}(P_{m})>T_{\text{GS}}$, $T_{\text{GS}}=0.9$. Such a simple
method will significantly alleviate the over-saturation issues and facilitate
brightness equalization.

##  5 Experiments

###  5.1 Implementation Details

We implement the GCS with PyTorch and train it on an A800 GPU with the Adam
optimizer. Some hyperparameters (the learning rates, camera positions,
rendering resolution, _etc_.) are similar to that in [17]. We use 5000 epochs
as [43] for total training iterations, which takes about one hour per scene.

Time schedule. In the experiment, $t$ is sampled from a uniform distribution
$\mathcal{U}(20,500+\delta_{\text{warm}})$, where $\delta_{\text{warm}}$ is
linearly decreasing from $480$ to $0$ in the first 1500 epochs. $s=t-\delta$,
where $\delta=100$ for most cases. $e$ is sampled from a uniform distribution
as $\mathcal{U}(s-\delta,s-\frac{\delta}{10})$.

Initialization. We apply Shap-E [11] and Point-E [27] to initialize the 3D
Gaussians, which are widely used in 3DGS-based text-to-3D generation [17, 44].

Figure 4: Qualitative comparison among the proposed and other methods on text-
to-3D generation results. From left to right, results generated by DreamFusion
[29], GaussianDreamer [46], ProlificDreamer [43], LucidDreamer [17], and the
proposed method, with a CFG weight $100$, $100$, $7$, $7$, $7$, respectively.
For each sub-figure, left: main view, right-top: back view, right-bottom:
normal/depth map of the 3D asset.

###  5.2 Text-to-3D Generation

Qualitative Comparison. We have showcased diverse views of the 3D assets
generated by our versatile approach, indicating that we can not only generate
highly detailed figures but also create reasonable outputs to align with the
complex prompt (results shown in the first row). To comprehensively assess the
efficacy of our proposed Guided Conditional Sampling (GCS), we conducted a
comparative analysis against the current state-of-the-art in GS-based [17, 46]
and baseline NeRF-based [29, 43] methods in text-to-3D generation, as shown in
Fig. 4. To ensure a fair comparison, all listed methods implement Stable
Diffusion 2.1 as the base model. Other hyperparameters were configured
following the default settings of the respective methods. The results indicate
that previous methods often struggled with insufficient details, prominent
artifacts (_e.g._ , Janus problem [1]), or over-saturation. In contrast, our
approach exhibits notable improvements in detail (_e.g._ , the armor of the
cat), fidelity, and exposure. Specifically, we can generate highly detailed
textures, achieve photorealistic effects (such as lights on the cat’s armor),
and maintain more consistent colors (such as the cat’s fur color) even with a
low CFG weight, illustrating the effectiveness of our proposed GCS and the
brightness-equalization techniques employed during training. Additional
results can be found in the Appendix.

Quantitative Comparison. We present the average CLIP Score, FID Score, and
user preference of five comparative methods [29, 43, 17, 39, 46] and the
proposed GCS on 120 generated views across 30 prompts selected from the
DreamFusion gallery666https://dreamfusion3d.github.io/gallery.html in Table 2.
For CLIP Score computation, we follow the steps presented in [29]. Results
show that our performance is comparable to that of VSD[43] in the evaluation
of prompt alignment, with much fewer instances of Janus problems [1], as
evidenced in the qualitative comparison shown in Fig. 4. The proposed approach
exhibits improved 3D consistency and fidelity for the 3D asset, resulting in a
higher user preference in prompt alignment.

For FID, we follow similar steps in [43] to calculate FID between 120 views of
3D object777Views are generated with fixed elevation ($0^{\circ}$, 3.6k views
generated in total) and varying azimuth (uniformly covering $360^{\circ}$) and
50k Stable Diffusion 2.1 generated images. We implement Perp-Neg when
necessary for different objects. The results show that the generated views of
the proposed method are more similar to the prior distribution compared to
other methods, indicating that the proposed GCS reduces distillation error.

User Study. We further conduct a user study among 30 volunteers for a more
comprehensive evaluation. Specifically, we asked the volunteers to evaluate
the generation quality regarding brightness (Q1), prompt alignment (Q2), and
fidelity (Q3). Those volunteers are also required to indicate their preference
based on rendered $360^{\circ}$ videos of 5 objects randomly sampled from 30
examples within six methods. We shuffled the presented order of the generated
results to avoid any form of leakage. The results of user preference in
percentage form shown in Table 2 indicate that our method performs best in all
aspects. An example question can be found in the Appendix.

Table 2: Quantitative comparison regarding CLIP Score, FID Score, and user
preference on three given questions (Q1, Q2, and Q3). The bold (underline)
number indicates the best (second-best) results.

| GaussianDreamer | DreamGaussian | DreamFusion | LucidDreamer | ProlificDreamer | Ours
---|---|---|---|---|---|---
CLIP Score$\uparrow$ | 30.29 | 28.65 | 30.68 | 31.30 | 33.17 | 32.37
FID Score$\downarrow$ | 133.48 | 215.89 | 137.22 | 109.57 | 119.53 | 103.40
User Preference: Q1$\uparrow$1 | 9.47 | 1.05 | 6.32 | 24.21 | 12.63 | 46.32
User Preference: Q2$\uparrow$2 | 10.53 | 1.05 | 6.32 | 30.53 | 7.37 | 44.21
User Preference: Q3$\uparrow$3 | 9.47 | 2.11 | 6.32 | 26.32 | 11.58 | 44.21

  * 1

Q1: From the perspective of color brightness, which of the following methods
produces the most balanced brightness (_e.g._., no over-saturation, moderate
saturation)?

  * 2

Q2: From the perspective of prompt alignment, which of the following methods
align most with the prompt?

  * 3

Q3: From the perspective of fidelity, which of the following methods produces
the most realistic objects?

Figure 5: Ablation study of proposed components.LucidDreamer [17] serves as
the baseline, we demonstrate the results under settings: (a) LucidDreamer [17]
\+ BEG, (b) $\mathcal{L}_{\mathrm{CC}}(\xi)+\mathcal{L}_{\mathrm{CG}}(\xi)$,
(c) $\mathcal{L}_{\mathrm{GCS}}(\xi)$, and (d) full mode
($\mathcal{L}_{\mathrm{GCS}}(\xi)$\+ BEG) from left to right.  Figure 6:
Ablation study of hyperparameters’ effects (left: $\delta$, middle:
$T_{\mathrm{GS}}$, right: $T_{\mathrm{B}}$)

###  5.3 Ablation Study

We conducted an ablation study to assess the effects of parameter setup
(including $\delta$, $T_{\mathrm{GS}}$, and $T_{\mathrm{B}}$), the proposed
Guided Consistency Sampling (GCS) loss, and the brightness-equalized
generation method (BEG).

Effect of time interval $\delta$ is evaluated by an ablation study on $\delta$
shown in Fig. 6. We find that large $\delta$ causes over-smoothness (_e.g._ ,
low level of detail on the strawberry’s surface), while small $\delta$ causes
color distortion (_e.g._ , unrealistic color in strawberry). $100$ is set to
generate visual-pleasant results.

Effect of Different Loss and BEG888We conduct additional ablation studies
regarding CC and CG to analyze the individual effect on generated 3D assets in
the Appendix.. As illustrated in Fig. 5, we compared the full model’s
($\mathcal{L}_{\mathrm{GCS}}(\xi)$ \+ BEG) generated results with those from
LucidDreamer [17], and two alternative models:
$\mathcal{L}_{\mathrm{CC}}(\xi)+\mathcal{L}_{CG}(\xi)$ and
$\mathcal{L}_{\mathrm{GCS}}(\xi)$ without BEG method, with a CFG weight set to
$7.5$. Compared to LucidDreamer [17], the full model successfully generated
more intricate details (_e.g._ , armor’s patterns and higher armor coverage).
While there was a slight alleviation in color distortion (inconsistency of fur
color between the back and front of the cat), the issue may persist.
Consequently, we introduced $\mathcal{L}_{\text{CP}}$ to mitigate color
distortion further (comparing
$\mathcal{L}_{\mathrm{CC}}(\xi)+\mathcal{L}_{\mathrm{CG}}(\xi)$ and
$\mathcal{L}_{\mathrm{GCS}}(\xi)$).

However, we observed a significant increase in overall brightness during
optimization. The implementation of the BEG method notably alleviates this
issue, as evidenced in the qualitative comparison between
$\mathcal{L}_{\mathrm{GCS}}(\xi)$ and the full model in Fig. 5. We find that
BEG will only affect the overall brightness, but not the fidelity, as shown in
a qualitative comparison between LucidDreamer [17] and LucidDreamer [17] \+
BEG. The effect of BEG is controlled by $T_{\text{B}}$ and $T_{\text{GS}}$.
Specifically, large (small) $T_{\text{B}}$ causes over-saturation (color
distortion) results (see the comparison in Fig. 6). $T_{\text{B}}=0.8$ works
for general cases. Small $T_{\text{GS}}$ will reset the brightness too
frequently to cause artifacts, $T_{\text{GS}}=0.9$ is a suitable setup.

##  6 Conclusion

In this work, we connect consistency distillation to score distillation. From
this connection, we propose Guided Consistency Sampling (GCS), an optimization
framework that includes three parts: Compact Consistency (CC) loss for
improved generator loss, Conditional Guidance (CG) score to enhance
conditional guidance, and Constraints in the Pixel domain (CP) for improved
fidelity. In addition, we innovate the Brightness-equalized Generation (BEG)
to tackle the over-saturation issue in 3DGS training. The proposed approach
improves the details, quality, and lighting effects of the generated 3D
assets.

## Acknowledgement

This work is supported by Rapid-Rich Object Search (ROSE) Lab, Nanyang
Technological University, Singapore, and the State Key Lab of Brain-Machine
Intelligence, Zhejiang University, Hangzhou, China.

## References

  * [1] Armandpour, M., Zheng, H., Sadeghian, A., Sadeghian, A., Zhou, M.: Re-imagine the negative prompt algorithm: Transform 2d diffusion into 3D, alleviate janus problem and beyond. arXiv preprint arXiv:2304.04968 (2023)
  * [2] Bensadoun, R., Kleiman, Y., Azuri, I., Harosh, O., Vedaldi, A., Neverova, N., Gafni, O.: Meta 3d texturegen: Fast and consistent texture generation for 3d objects. arXiv preprint arXiv:2407.02430 (2024)
  * [3] Burley, B., Studios, W.D.A.: Physically-based shading at disney. In: ACM SIGGRAPH (2012)
  * [4] Chen, R., Chen, Y., Jiao, N., Jia, K.: Fantasia3d: Disentangling geometry and appearance for high-quality text-to-3D content creation. Int. Conf. Comput. Vis. (2023)
  * [5] Chen, Y., Zhang, C., Yang, X., Cai, Z., Yu, G., Yang, L., Lin, G.: It3D: Improved text-to-3D generation with explicit view synthesis. In: AAAI (2024)
  * [6] Chen, Y., Georgiou, T.T., Pavon, M.: On the relation between optimal transport and schrödinger bridges: A stochastic control viewpoint. Journal of Optimization Theory and Applications (2016)
  * [7] Chen, Z., Wang, F., Wang, Y., Liu, H.: Text-to-3D using gaussian splatting. In: IEEE Conf. Comput. Vis. Pattern Recog. (2024)
  * [8] Deng, K., Omernick, T., Weiss, A., Ramanan, D., Zhu, J.Y., Zhou, T., Agrawala, M.: Flashtex: Fast relightable mesh texturing with lightcontrolnet. arXiv preprint arXiv:2402.13251 (2024)
  * [9] Ho, J., Jain, A., Abbeel, P.: Denoising diffusion probabilistic models. Adv. Neural Inform. Process. Syst. (2020)
  * [10] Ho, J., Salimans, T.: Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598 (2022)
  * [11] Jun, H., Nichol, A.: Shap-e: Generating conditional 3D implicit functions. arXiv preprint arXiv:2305.02463 (2023)
  * [12] Katzir, O., Patashnik, O., Cohen-Or, D., Lischinski, D.: Noise-free score distillation. arXiv preprint arXiv:2310.17590 (2023)
  * [13] Kerbl, B., Kopanas, G., Leimkühler, T., Drettakis, G.: 3D gaussian splatting for real-time radiance field rendering. ACM Trans. Graph. (2023)
  * [14] Kim, D., Lai, C.H., Liao, W.H., Murata, N., Takida, Y., Uesaka, T., He, Y., Mitsufuji, Y., Ermon, S.: Consistency trajectory models: Learning probability flow ode trajectory of diffusion. Int. Conf. Learn. Represent. (2024)
  * [15] Léonard, C.: A survey of the schr$\backslash$" odinger problem and some of its connections with optimal transport. arXiv preprint arXiv:1308.0215 (2013)
  * [16] Li, Z., Zheng, Q., Shi, B., Pan, G., Jiang, X.: Dani-net: Uncalibrated photometric stereo by differentiable shadow handling, anisotropic reflectance modeling, and neural inverse rendering. In: IEEE Conf. Comput. Vis. Pattern Recog. (2023)
  * [17] Liang, Y., Yang, X., Lin, J., Li, H., Xu, X., Chen, Y.: Luciddreamer: Towards high-fidelity text-to-3D generation via interval score matching. arXiv preprint arXiv:2311.11284 (2023)
  * [18] Lin, C.H., Gao, J., Tang, L., Takikawa, T., Zeng, X., Huang, X., Kreis, K., Fidler, S., Liu, M.Y., Lin, T.Y.: Magic3D: High-resolution text-to-3D content creation. In: IEEE Conf. Comput. Vis. Pattern Recog. (2023)
  * [19] Liu, R., Wu, R., Van Hoorick, B., Tokmakov, P., Zakharov, S., Vondrick, C.: Zero-1-to-3: Zero-shot one image to 3D object. In: Int. Conf. Comput. Vis. (2023)
  * [20] Lu, C., Zhou, Y., Bao, F., Chen, J., Li, C., Zhu, J.: Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps. Adv. Neural Inform. Process. Syst. (2022)
  * [21] Lu, C., Zhou, Y., Bao, F., Chen, J., Li, C., Zhu, J.: Dpm-solver++: Fast solver for guided sampling of diffusion probabilistic models. arXiv preprint arXiv:2211.01095 (2022)
  * [22] Luo, S., Tan, Y., Huang, L., Li, J., Zhao, H.: Latent consistency models: Synthesizing high-resolution images with few-step inference. arXiv preprint arXiv:2310.04378 (2023)
  * [23] McAllister, D., Ge, S., Huang, J.B., Jacobs, D.W., Efros, A.A., Holynski, A., Kanazawa, A.: Rethinking score distillation as a bridge between image distributions. arXiv preprint arXiv:2406.09417 (2024)
  * [24] Metzer, G., Richardson, E., Patashnik, O., Giryes, R., Cohen-Or, D.: Latent-NeRF for shape-guided generation of 3D shapes and textures. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 12663–12673 (2023)
  * [25] Mildenhall, B., Srinivasan, P.P., Tancik, M., Barron, J.T., Ramamoorthi, R., Ng, R.: NeRF: Representing scenes as neural radiance fields for view synthesis. Eur. Conf. Comput. Vis. (2021)
  * [26] Mokady, R., Hertz, A., Aberman, K., Pritch, Y., Cohen-Or, D.: Null-text inversion for editing real images using guided diffusion models. 2023 ieee. In: CVF Conference on Computer Vision and Pattern Recognition (CVPR). pp. 6038–6047 (2022)
  * [27] Nichol, A., Jun, H., Dhariwal, P., Mishkin, P., Chen, M.: Point-e: A system for generating 3D point clouds from complex prompts. arXiv preprint arXiv:2212.08751 (2022)
  * [28] Pham, H.A.: Reduction of function evaluation in differential evolution using nearest neighbor comparison. Vietnam Journal of Computer Science (2015)
  * [29] Poole, B., Jain, A., Barron, J.T., Mildenhall, B.: Dreamfusion: Text-to-3D using 2d diffusion. In: Int. Conf. Learn. Represent. (2022)
  * [30] Rombach, R., Blattmann, A., Lorenz, D., Esser, P., Ommer, B.: High-resolution image synthesis with latent diffusion models. In: IEEE Conf. Comput. Vis. Pattern Recog. (2022)
  * [31] Saharia, C., Chan, W., Saxena, S., Li, L., Whang, J., Denton, E.L., Ghasemipour, K., Gontijo Lopes, R., Karagol Ayan, B., Salimans, T., et al.: Photorealistic text-to-image diffusion models with deep language understanding. Adv. Neural Inform. Process. Syst. (2022)
  * [32] Sauer, A., Lorenz, D., Blattmann, A., Rombach, R.: Adversarial diffusion distillation. arXiv preprint arXiv:2311.17042 (2023)
  * [33] Seo, J., Jang, W., Kwak, M.S., Kim, H., Ko, J., Kim, J., Kim, J.H., Lee, J., Kim, S.: Let 2d diffusion model know 3D-consistency for robust text-to-3D generation. arXiv preprint arXiv:2303.07937 (2023)
  * [34] Shen, T., Gao, J., Yin, K., Liu, M.Y., Fidler, S.: Deep marching tetrahedra: a hybrid representation for high-resolution 3D shape synthesis. Adv. Neural Inform. Process. Syst. (2021)
  * [35] Shi, Y., Wang, P., Ye, J., Long, M., Li, K., Yang, X.: Mvdream: Multi-view diffusion for 3D generation. arXiv preprint arXiv:2308.16512 (2023)
  * [36] Song, J., Meng, C., Ermon, S.: Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 (2020)
  * [37] Song, Y., Dhariwal, P., Chen, M., Sutskever, I.: Consistency models. arXiv preprint arXiv:2303.01469 (2023)
  * [38] Song, Y., Sohl-Dickstein, J., Kingma, D.P., Kumar, A., Ermon, S., Poole, B.: Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13456 (2020)
  * [39] Tang, J., Ren, J., Zhou, H., Liu, Z., Zeng, G.: Dreamgaussian: Generative gaussian splatting for efficient 3D content creation. arXiv preprint arXiv:2309.16653 (2023)
  * [40] Tang, J., Wang, T., Zhang, B., Zhang, T., Yi, R., Ma, L., Chen, D.: Make-it-3D: High-fidelity 3D creation from a single image with diffusion prior. In: IEEE Conf. Comput. Vis. Pattern Recog. (2023)
  * [41] Tsalicoglou, C., Manhardt, F., Tonioni, A., Niemeyer, M., Tombari, F.: Textmesh: Generation of realistic 3D meshes from text prompts. In: Int. Conf. on 3D Vision (3DV) (2024)
  * [42] Wang, H., Du, X., Li, J., Yeh, R.A., Shakhnarovich, G.: Score jacobian chaining: Lifting pretrained 2d diffusion models for 3D generation. In: IEEE Conf. Comput. Vis. Pattern Recog. (2023)
  * [43] Wang, Z., Lu, C., Wang, Y., Bao, F., Li, C., Su, H., Zhu, J.: Prolificdreamer: High-fidelity and diverse text-to-3D generation with variational score distillation. Adv. Neural Inform. Process. Syst. (2024)
  * [44] Wu, Z., Zhou, P., Yi, X., Yuan, X., Zhang, H.: Consistent3D: Towards consistent high-fidelity text-to-3D generation with deterministic sampling prior. arXiv preprint arXiv:2401.09050 (2024)
  * [45] Yang, X., Chen, Y., Chen, C., Zhang, C., Xu, Y., Yang, X., Liu, F., Lin, G.: Learn to optimize denoising scores for 3D generation: A unified and improved diffusion prior on NeRF and 3D gaussian splatting. arXiv preprint arXiv:2312.04820 (2023)
  * [46] Yi, T., Fang, J., Wu, G., Xie, L., Zhang, X., Liu, W., Tian, Q., Wang, X.: Gaussiandreamer: Fast generation from text to 3D gaussian splatting with point cloud priors. IEEE Conf. Comput. Vis. Pattern Recog. (2024)
  * [47] Yu, X., Guo, Y.C., Li, Y., Liang, D., Zhang, S.H., Qi, X.: Text-to-3D with classifier score distillation. arXiv preprint arXiv:2310.19415 (2023)
  * [48] Zhang, H., Chen, B., Yang, H., Qu, L., Wang, X., Chen, L., Long, C., Zhu, F., Du, D., Zheng, M.: Avatarverse: High-quality & stable 3D avatar creation from text and pose. In: AAAI (2024)
  * [49] Zhang, J., Zhang, X., Zhang, H., Liew, J.H., Zhang, C., Yang, Y., Feng, J.: Avatarstudio: High-fidelity and animatable 3D avatar creation from text. arXiv preprint arXiv:2311.17917 (2023)
  * [50] Zhang, Q., Chen, Y.: Fast sampling of diffusion models with exponential integrator. arXiv preprint arXiv:2204.13902 (2022)
  * [51] Zheng, J., Hu, M., Fan, Z., Wang, C., Ding, C., Tao, D., Cham, T.J.: Trajectory consistency distillation. arXiv preprint arXiv:2402.19159 (2024)
  * [52] Zhou, Z., Tulsiani, S.: Sparsefusion: Distilling view-conditioned diffusion for 3D reconstruction. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 12588–12597 (2023)
  * [53] Zhu, J., Zhuang, P.: Hifa: High-fidelity text-to-3D with advanced diffusion guidance. arXiv preprint arXiv:2305.18766 (2023)

## Appendix

In this appendix,

  1. 1.

we provide some discussions about the limitations of our method and the
failure cases;

  2. 2.

we show an example question for the user study in Sec. 0.B;

  3. 3.

we visualize the accumulated brightness during optimization in Sec. 0.C;

  4. 4.

we provide a detailed proof of Lemma 1 in Sec. 0.D that clarifies the
effectiveness of the proposed Compact Consistency (CC) loss;

  5. 5.

we show more ablation studies regarding CC and Conditional Guidance (CG) loss
in Sec. 0.E; we also show the effect of high order ODE solver in this section;

  6. 6.

we showcase more results generated by the proposed Guided Consistency Sampling
(GCS) in Sec. 0.F.

##  Appendix 0.A Limitations

The proposed GCS exhibits shortcomings in addressing Janus issues, which we
attribute to the inherent inconsistencies in pre-trained models under multi-
view conditions. Also, it doesn’t perform well on compositional prompts.
Moreover, our approach necessitates extensive training in the GS model,
ranging from 3000 to 5000 epochs, translating to 35-60 minutes for rendering a
single object. These limitations show a significant gap in practical
application.

Failure case I: Janus Problem. Despite proposing multiple strategies to
improve the overall generation quality, our method still suffers from the
Janus problem and occasionally generates multi-view inconsistent results (Fig.
7). A solution is to change the random seed or give a better initialization.

Figure 7: Failure case I. The 3D asset is affected by the Janus problem.

Failure case II: Compositional Prompt. Our method performs poorly in
generating high-quality compositional objects (Fig. 8), possibly due to a bad
initialization with insufficient Gaussian points to model different components
or a lack of relevant techniques to combine those components correctly. We
regard improving this as a future work.

Figure 8: Failure case II. The 3D assets are generated based on a
compositional prompt.

##  Appendix 0.B Example Question

We show an example question from our user study. We use Google Forms to
collect the volunteers’ responses.

Figure 9: Example questions used in the user study.

##  Appendix 0.C Visualization of Accumulated Brightness

We show an example of accumulated brightness during the generation process of
the proposed method without BEG in Fig. 10.

Figure 10: An illustration of brightness accumulation. The highlight point
(red box) in early-stage training will be kept and spread to its surroundings,
causing over-saturation.

##  Appendix 0.D Proof of Lemma 1

######  Lemma 2 ([51, 37, 14, 44])

Let $\Delta t=\max\left\\{\left|\delta_{k}\right|\right\\}$,
$k\in[0,...,n_{s}]$, where $n_{s}$ is the index of $\delta$ at time step $s$,
and $F_{\theta}(\cdot,\cdot)$ is the origin prediction function grounded on
the empirical PF-ODE. Assume $F_{\theta}$ satisfies the Lipschitz condition,
if there is a ${\mathbf{x}}_{\pi}$ satisfying $\mathcal{L}_{\rm{CC}}(\xi)=0$,
given an image ${\mathbf{x}}_{0}\sim p_{\text{data}}({\mathbf{x}})$, for any
$t,s,e\in[\\![0,...,T]\\!]$ with $t>s>e$, we have:

$\begin{split}\mathop{\textnormal{sup}}\limits_{t,s,{\mathbf{x}}_{\pi}}\|\hat{{\mathbf{x}}}_{\\{\pi,e\\}},\hat{{\mathbf{x}}}_{\\{0,e\\}}\|_{2}=\mathcal{O}\left((\Delta
t)^{p}\right)(T-e),\end{split}$ (26)

$\hat{{\mathbf{x}}}_{\\{0,e\\}}$ is the distribution of ${\mathbf{x}}$
diffused to time $e$, $p$ is the order of the ODE solver.

###### Proof

Given $\mathcal{L}_{\rm{CC}}(\xi)=0$, for any $\pi$, $t,s$, and $e$, we have:

$G_{\theta}\left(\hat{\mathbf{x}}_{\\{\pi,t\\}};t,e,y\right)\equiv
G_{\theta}\left(\hat{\mathbf{x}}_{\\{\pi,s\\}};s,e,y\right).$ (27)

Defining $\hat{\mathbf{x}}_{\\{\pi,t_{k}\\}}=\mathbf{x}_{t_{k}}$ for
simplicity, Eq. 27 can be rewritten as:

$G_{\theta}\left(\mathbf{x}_{s};s,e,y\right)\equiv
G_{\theta}\left({\mathbf{x}}_{t};t,e,y\right),$ (28)

where, ${\mathbf{x}}_{t}$ is obtained by $\hat{{\mathbf{x}}}_{s}$ through DDIM
inversion. For a more general expression, we represent distillation error [44]
at $t_{k}>e$ as:

$e^{t_{k}}_{e}=G_{\theta}(\mathbf{x}_{t_{k}};t_{k},e,y)-\hat{\mathbf{x}}_{\\{0,e\\}}.$
(29)

It is straightforward that at the boundary timestep $e$, the error is,

$e^{e}_{e}=\hat{\mathbf{x}}_{\\{\pi,e\\}}-\hat{\mathbf{x}}_{\\{0,e\\}}.$ (30)

We then derive $e^{t_{k}}_{e}$ at $t_{k}$ as:

$\displaystyle\begin{aligned}
\bm{e}^{t_{k}}_{e}=&G_{\theta}\left(\mathbf{x}_{t_{k}};t_{k},e,y\right)-\hat{\mathbf{x}}_{\\{0,e\\}},\\\
=&G_{\theta}\left(\bar{\mathbf{x}}_{\\{t_{k}\rightarrow
t_{k+1}\\}};t_{k+1},e,y\right)-\hat{\mathbf{x}}_{\\{0,e\\}},\\\
=&G_{\theta}\left(\bar{\mathbf{x}}_{\\{t_{k}\rightarrow
t_{k+1}\\}};t_{k+1},e,y\right)-G_{\theta}\left(\mathbf{x}_{t_{k+1}};t_{k+1},e,y\right)+G_{\theta}\left(\mathbf{x}_{t_{k+1}};t_{k+1},e,y\right)-\hat{\mathbf{x}}_{\\{0,e\\}},\\\
=&G_{\theta}\left(\bar{\mathbf{x}}_{\\{t_{k}\rightarrow
t_{k+1}\\}};t_{k+1},e,y\right)-G_{\theta}\left(\mathbf{x}_{t_{k+1}};t_{k+1},e,y\right)+\bm{e}_{e}^{t_{k+1}}.\end{aligned}$
(31)

According to Lipschitz condition on $G_{\theta}$, we derive:

$\displaystyle\begin{aligned}
\left\|\bm{e}^{t_{k}}_{e}\right\|&\leq\left\|G_{\theta}\left(\bar{\mathbf{x}}_{\\{t_{k}\rightarrow
t_{k+1}\\}};t_{k+1},e,y\right)-G_{\theta}\left(\mathbf{x}_{t_{k+1}};t_{k+1},e,y\right)\right\|+\left\|\bm{e}^{t_{k+1}}_{e}\right\|,\\\
&\leq L\left\|\bar{\mathbf{x}}_{\\{t_{k}\rightarrow
t_{k+1}\\}}-\mathbf{x}_{t_{k+1}}\right\|+\left\|\bm{e}^{t_{k+1}}_{e}\right\|,\\\
&\stackrel{{\scriptstyle(i)}}{{=}}\left\|\bm{e}^{t_{k+1}}_{e}\right\|+\mathcal{O}\left(\left(t_{k}-t_{k+1}\right)^{p+1}\right),\end{aligned}$
(32)

where $(i)$ hold according to the local error of Euler solver [44, 37].
Iteratively, we can obtain the upper bound of distillation error at $e$:

$\displaystyle\begin{aligned}
\left\|\bm{e}^{e}_{e}\right\|_{2}&\leqslant\sum_{k=n_{e}}^{N-1}\mathcal{O}\left(\left(t_{k+1}-t_{k}\right)^{p+1}\right)+\|e^{T}_{e}\|,\\\
&\stackrel{{\scriptstyle(ii)}}{{\approx}}\sum_{k=n_{e}}^{N-1}\left(t_{k+1}-t_{k}\right)\mathcal{O}\left((\Delta
t)^{p}\right),\\\ &=\mathcal{O}\left((\Delta
t)^{p}\right)\sum_{k=n_{e}}^{N-1}\left(t_{k+1}-t_{k}\right),\\\
&=\mathcal{O}\left((\Delta t)^{p}\right)\left(T-e\right),\\\ \end{aligned}$
(33)

where $N$ is the index of time $T$, $(ii)$ holds because $\|e^{T}_{e}\|$
describes the KL divergence between $\mathbf{x}_{0}$ and
$G_{\theta}\left(\hat{\mathbf{x}}_{\\{\pi,T\\}};T,e,y\right)$, where
$\hat{\mathbf{x}}_{\\{\pi,T\\}}$ follows the normal distribution. For a well-
trained diffusion model, $\|e^{T}_{e}\|$ should be bounded and remain constant
at $e$, which can be ignored. The proof is completed.

According to Lemma. 2, we prove that the proposed CC loss will converge within
a lower error bound than CDS loss in [44] when $e>0$.

##  Appendix 0.E Additional Ablation Studies

Effect of CC and CG. We conduct additional ablation studies to evaluate the
effect of $\mathcal{L}_{\text{CC}}$ and $\mathcal{L}_{\text{CG}}$.
Specifically, we compare $\mathcal{L}_{\text{CC}}+\mathcal{L}_{\text{CG}}$
with $\mathcal{L}_{\text{ISD}}$ (LucidDreamer [17]),
$\mathcal{L}_{\text{CG}}$, and
$\mathcal{L}_{\text{CG}}+\mathcal{L}^{0}_{\text{CC}}$, where we note
$\mathcal{L}^{0}_{\text{CC}}$ as $\mathcal{L}_{\text{CC}}$ with $e\equiv 0$.
As shown in Fig. 11, we find the proposed $\mathcal{L}_{\text{CG}}$ has higher
generation quality compared to the LucidDreamer. $\mathcal{L}_{\text{CC}}$
will further add more details to the generated results in the generated 3D
asset. Comparing with $\mathcal{L}_{\text{CG}}+\mathcal{L}^{0}_{\text{CC}}$
that shares the same distillation error bound with CDS [44], we found the
color distortion becomes more severe and tend to be over-exposed, validating
the effect of proposed $\mathcal{L}_{\text{CC}}$ in reducing distillation
error.

Figure 11: Qualitative comparison regarding different variances of
$\mathcal{L}_{\text{CC}}$ and $\mathcal{L}_{\text{CG}}$. From left to right,
3D asset generated by $\mathcal{L}_{\text{ISD}}$, $\mathcal{L}_{\text{CG}}$,
$\mathcal{L}_{\text{CG}}+\mathcal{L}_{\text{CC}}^{0}$, and
$\mathcal{L}_{\text{CG}}+\mathcal{L}_{\text{CC}}$, respectively.

Effect of High Order ODE-Solver. We try 2nd order DPM-Solver at denoising
steps, and the results indicate differences in illumination and details, as
shown in Fig. 12.

[capbesideposition=right,top]figure[]

Figure 12: Generated views of GCS+BEG under a low CFG weight ($w=7.5$) by
using first-order (right) and second-order DPM-Solver.

##  Appendix 0.F Additional Qualitative Evaluation

In this section, we show more quality comparison between the proposed GCS,
DreamFusion [29], GaussianDreamer [46], ProlificDreamer [43], and LucidDreamer
[17] in Fig. 13.

Figure 13: Additional qualitative comparison among DreamFusion [29] (column
1), GaussianDreamer [46] (column 2), ProlificDreamer [43] (column 3),
LucidDreamer [17] (column 4), and our method (column 5).