Training Unbiased Diffusion Models From Biased Dataset
Authors: Yeongmin Kim
Byeonghu Na
Minsang Park
JoonHo Jang
Dongjun Kim
Wanmo Kang
Il-chul Moon
Venue: ICLR 2024 poster (2024)
Keywords: diffusion model
density ratio estimation
dataset bias
Primary area: generative models
TL;DR: We propose time-dependent importance reweighting to mitigate dataset bias in diffusion models.

Abstract: With significant advancements in diffusion models, addressing the potential risks of dataset bias becomes increasingly important. Since generated outputs directly suffer from dataset bias, mitigating latent bias becomes a key factor in improving sample quality and proportion. This paper proposes time-dependent importance reweighting to mitigate the bias for the diffusion models. We demonstrate that the time-dependent density ratio becomes more precise than previous approaches, thereby minimizing error propagation in generative learning. While directly applying it to score-matching is intractable, we discover that using the time-dependent density ratio both for reweighting and score correction can lead to a tractable form of the objective function to regenerate the unbiased data density. Furthermore, we theoretically establish a connection with traditional score-matching, and we demonstrate its convergence to an unbiased distribution. The experimental evidence supports the usefulness of the proposed method, which outperforms baselines including time-independent importance reweighting on CIFAR-10, CIFAR-100, FFHQ, and CelebA with various bias settings. Our code is available at https://github.com/alsdudrla10/TIW-DSM.

Published as a conference paper at ICLR 2024
TRAINING UNBIASED DIFFUSION MODELS FROM BIASED DATASET
Yeongmin Kim- Byeonghu Na', Minsang Park', JoonHo Jang', Dongjun Kim', Wanmo Kang', II-Chul Moon
ABSTRACT
With significant advancements in diffusion models, addressing the potential risks of dataset bias becomes increasingly important. Since generated outputs directly suffer from dataset bias, mitigating latent bias becomes a key factor in improv- ing sample quality and proportion. This paper proposes time-dependent impor- tance reweighting to mitigate the bias for the diffusion models. We demonstrate that the time-dependent density ratio becomes proaches, thereby minimizing error propagation in generative learning. While directly applying it score-matching is intractable, we discover that using the time-dependent density ratio both for reweighting and score correction can lead tractable form of the objective function regenerate the unbiased data density. Furthermore, we theoretically establish a connection with traditional matth-ma, and we demonstrate its convergence to an unbiased distribu- tion. The experimental evidence supports the usefulness of the proposed method, which outperforms baselines including time-independent importance reweighting on CIFAR-10, 10, CIFAR-100, FFHQ, and CelebA with various bias settings. Our code is available at https:://////. /ttpps:/gittaee hwg.ghtthuuuu..g com httmm/assdddraa//11raa -DSM
precise than previous ap-
INTRODUCTION
Recent developments on diffusion models (Song et al. 2020 Ho et al. 2020) make it possible to generate high-fidelity images (Dhariwal & Nichol| 2021| Kim et al. 2023] and dominate generative learning frameworks. The diffusion models deliver promising sample quality in various applications, i.e. text-to-image generation (Rombach et al.) 2022 Nichol et al. 2022), image-to-image translation (Meng et al. 2201; Zhou et al.) 2024), and counterfactual generation (Kim et al., 20226 Wang al.) 2023a). As diffusion models become increasingly prevalent, addressing the potential risks its dataset bias becomes more crucial, which had been less studied in the generative model community.
The dataset bias is pervasive in real world datasets, which ultimately affects the behavior of machine learning systems (Tommasi et al.) 2017). As shown in Figure Iaj there exists a bias in the sensitive attribute in the CelebA (Liu et al. 2015) benchmark dataset. In generative modeling, the statistics of generated samples are directly influenced or even exacerbated by dataset bias (Hall et al., 2022] Frankel & Vendrow 2020). The underlying bias factor is often left unannotated (Torralba & Efros 2011). so is a challenge to mitigate the bias in an unsupervised manner. Importance reweighting is one of the standard training techniques for de-biasing in generative models. Choi al. (2020) pro-
pose pioneering work in generative modeling by utilizing a pre-trained density ratio between biased and unbiased distributions. However, the estimation of density ratio notably imprecise (Rhodes et al. 2020), leading to eтror propagation in training generative models.
We introduce method called Time-dependent Importance Weightting (TIW), designed for diffu- sion models. This method estimates the dime-dependent density ratio between the perturbed biased distribution and the perturbed unbiased distribution using a time-dependent diseriminator. We inves- tigate the perturbation provides benefits for accurate estimation of the density ratio. We introduce that the time-dependent density ratio can serve as a weighting mechanism, as well as a score cor- rection. By utilizing these dual roles by density ratios, simultaneously; we render the objective function tractable and establish a theoretical equivalence with existing sctre-matching objectives from unbiased distributions.
"Coresponndence Ycongmin Kim @alsdudrla10@aann
KAIST, "Summary.Al

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Published as a conference paper at ICLR 2024
Female
Male Non-Rlack (29.6%)
Femaalo Black hair hair (11.5%% (12.4%)
Male
Female Non Black hair (31.0%)
Male Non: Dlack hair (27.8%)
Fermal Black hair (20.1%)
Male Black huir (21.1%)
Non-Black hair (46.5%)
(a) CelebA benchmark dataset
(b) Generated samples from proposed method
Figure I:
The samples that reflect the proportion of four latent subgroups. The proposed method mitigates the latent bias statistics as shown in (b).
We test our method on the CIFAR-10, CIFAR-100 (Krizhessky 2009). FFHQ Karras et al. 2019), and CelebA datasets. We observed our method outperforms the time-independent importance reweighting and naive baselines in various bias settings.
2
BACKGROUND
2.1
PROBLEM SETUP
The goal of generative modeling estimate the underlying true data distribution Paata : X - 1200 so this distribution enables likelihood evaluations and sample generations. In this process, we often consider an observed sample dataset, Dobs {x(1), x(.,x(()) with i.i.d. sampling of x(), from Pima to be unbiased with respect to the underlying latent factors, but this is not true if the sampling procedure is biased. Dan could be biased due to social, geographical, and physical factors resulting in deviations from the intended purposes. Subsequently, the parameter O of the modeled distribution pe X + R20 also becomes biased, which won't ton't converge Paata through learning O with Dabs-
Building upon prior research (Choi et al. 2020), we assume that the accessible data Dobs consists of two sets: Dobs Doias U Dret- The elements in D are i.i.d. samples from an unknown biased distribution Paias : X' + Rzo. Note that Pbias deviates from Pdata because its unknown sampling bias. Each element of Diet is i.i.d. sampled from Pdatas but [Dret] is relatively smaller than [Doas We also follow a weak supervision setting, which does not provide explicit bias in Pbias; but we assume that the origin of data instances is known to be either Dier Doius.
2.2 DIFFUSION MODEL AND SCORE MATCHING
This paper focuses on diffusion models to parameterize model distribution pg. The diffusion model well explained by Stochastic Differential Equations (SDEs) (Song et al., [2020] Anderson, 1982). For data random variable Xo Pdata: the forward process in eq. ① perturbs it into noise random variable XT. The reverse process in eq. 2 transforms noise random variable xy to Xg.
dx; f(x,, ()dt g(()dw
dx, [f(xx,, t) ga (t) log (x,) g(t)d
where w, denotes standard Wiener process, f(.,t): Rd R is a drift term, and g(-)
R
is diffusion term, we denotes the Wiener process when time flows backward, and p (x:) is the probability density function of x,. To construct the reverse process, the time-dependent score
function is approximated through a neural network Sp (x,,t) t) ~ V log PoogPin (xx). (X... The score-matching
objective is derived from the Fisher divergence (Song Ermon 2019) as described in eq. (3)
(' Epin (A(t)]ssoxx t) V log Plan (x:)1)ddr
(s Pdata) =
(3)
2
1
/'"" Byan Eptx. xx) ((())lso(xx |
LDSM Paata)
V Vlogp(x,(xo)))
(4)
2
where X()) [0, + R is a temporal weighting function. However, CsM is intractable because
computing V log Vanna (xx) from sample x, is impossible. To make score-matching tractable, LDSM
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commonly used objective function. LUsM only needs to calculate V log which comes from the forward process. Note that LUSM is equivalent to LsM up to a constant with respect to 0 Vincent 2011: Song & Ermon 2019).
2.3 DENSITY RATIO ESTIMATION
The density ratio estimation (DRE) through discriminative training (also known as noise contrastive estimation) (Gutmann & Hyvärinen 2010 SSugyymaa et al. 2012) is statistical technique that provides the likelihood ratio between two probability distributions. This estimation assumes that we can access samples from two distributions Pdaaa and Phias- Afterwards, we set pseudo labels = on samples from Pdata- and y = O on samples from Phias The discriminator dø :X' [0. 1]. which predicts such pseudo labels, can approximate the probability of label given X through
p(y 1|x,) dæ (Xx). The optimal discriminator o² arg ming (xo)] log dø (xo) +
Ep.. logo - dø (xo))]] represents the density ratio from the following relation in eq. 5 We
define wig- (Xo) as the true density ratio.
Wap (xo) : Patata (X))
(Xu)
p(xoly = 1) ply = 0)p(y 1 1xx)
dø (x5)
(5)
Phias XD) pxxoly =0 ply pp(y 0|xo)
(xx))
2.4 IMPORTANCE REWEIGHTING FOR UNBIASED GENERATIVE LEARNING
Choi et al. (2020) propose the importance reweighting to mitigate dataset bias. They originally
conducted experiment GANs (Goodfellow al. 2014 Brock et al. 2018). and there is no previous work on diffusion models with the same purpose.
Hence, the first approach would be utilizing the important reweighting for GANs the diffusion models. In detail, the previous work pre-trains the density ratio Piaa(Xo) (x(o)) as described in
PNu)(X))
Section 2.3 The density ratio assigns a higher weight to the sample that appears to be from Pdata
described in eq. (6). The optimally estimated density ratio makes possible to compute eq. (7)
This can lead the Pe to converge to the true data distribution by utilizing the biased dataset. We
call this method -ndeeendeenneett importance reweighting, and the derived objective in eq. as importance reweighted denoising motehia (IW-DSM).
L/" E Exnaa (xo))
Pdataa (Xo)
LDSM Pdaaa) =
Prius (xo) ldom (0, xo) dl
(6)
(" E E (Xa)
Ws- (dm) (6, xo) dt,
where fasm(() (0,x0) = Ep(x, xx) (s(x),) - V Vlogp(x//x01111
3 METHOD
In this section, we present our approach for training an unbiased diffusion model with weak super- vision setting. Section 3.1 explains the motivation behind time-dependent importance reweighting. Section [.2] explains the method in detail, which involves using a time-dependent density ratio for both weighting and score correction. Furthermore, we explore the relationship between our proposed objective and the previous score-matching objective.
3.1 WHY TIME-DEPENDENT IMPORTANCE REWEIGHTING?
Density ratio estimation (DRE) provides significant benefits for probabilistic machine learn- ing (Song & Kingmal 202T Aneja et al.) 2020; Xiao & Han 2022] Goodfellow et 2l,, How- ever, DRE suffers from estimation errors due to the density-cassm problem. Rhodes et al. (2020) state that the ratio estimation error increases when 1) the distance between two distributions is far. and 2) the number of samples from two distributions is small. The pre-trained density ratio from Section 2.4 Wig also suffers from this issue because 1) handle real-world datasets that are in high dimensions, and 2) the number of reference data [Drell would small. To address this prob- lem, we investigate method that involves using a time-dependent density ratio between perturbed
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Plas Dka)
Tree Rado
Extenadd
Extiratac
True Folio
MSE Hgo
Accumulated MSE gap
Gain:
Inpe nomighiie Hdepe dettriiight
%
4
%
Ralp
Rato
Timee
(a) Dias
(b) Deet
(c) f O, MSE=7.9
(d) f 0.4, MSE=3.8
(c) MSE varying t
Figure 2: Accuracy of density ratio estimation between Phias and Pdata under diffusion process. (a-b) Samples from two distributions. (c-d) Density ratio statisties the ground truth and the model, at each diffusion time. (e) Density ratio estimation error according to l. The density ratio error becomes significantly decreases as becomes larger.
distributions Phize (xx) and Panaa (xx). This has benefits: 1) The perturbation from the forward diffu- sion process makes the two distributions closer as I. becomes larger; and 2) the perturbation reduces Monte Carlo error sampling of each distribution. These two advantages of forward diffusion can contribute significantly to the accuracy of density ratio estimation.
The time-dependent density ratio w (xx) == (x)) is represented by a time-dependent discrim-
inator. We now parametrize the time-dependent discriminator dæ X' x [0, 7] + [0, 1] which separates the samples from (Xe) and the samples from (xi,) The time-dependent discrim- inator is optimized by minimizing temporally weighted binary cross-entropy (T-BCE) objective as described in eq. (8) where ((t) denotes temporal weighting function. We represent the time- de- (x..e)
dependent density ratio as w'' (xx) = I-d (Xe.))"
LT.RC Praata Prins) = ['" X(1) (pan ((1) (xx)) log dop (xe, ()] + Eygn (x,)) log(1 do (xe. [)
Paiata
(8)
Figure 2 shows the accuracy of density ratio estimation over the diffusion time interval 1 E 10, 7].
where T
We set the 2-D distributions as follows: Phius (Xo) == 9 Nxx;: (-2. I) +
1o. (xx:; (2, 2)T I) and pl (Xo) == [Nxox (-2, -2) II) + (xn; (2, 2 I). We sampled a finite number of samples from each distribution illustrated in Figures and 26 We perturb these
1
two distributions to Phina((x (xx) and v/r,,(xx,, following the Variance Preserving (VP) SDE (Ho et al.,
2020 [Song et al., 2020). Figures [2c
the histograms of the ground truth density ratio: w (x+), and the estimated density ratio: w'y (xe,, with x, drawn from 2 (Piiss + Pdmaa) At = O, the true ratio is determined by the choice of the mode. The discriminator tends to overconfident in favor of either Paias or Pdata. exhibiting skew toward either side (Figure 2c}. This phenomenon is mitigated as the diffusion time increases (Figure 2d). The mean squared error (MSE) is calculated through Eg (ninn +rin [1] (xx) - w (x,) 1 for each time step. Figure 2e illustrates that the density ratio estimation error decreases rapidly as increases.
Applying the lime-independent importance reweighting, as described in Choi et al. 2020), utilizes the density ratio only at t for loss computation, and this ratio becomes constant to in the score- matching. The previously discussed density-chasee creates the weight estimation error, illustrated as a red line in Figure 2e] and this error propagates through the diffusion model training. Con- sidering the time integrating nature of score-matching objectives, the integrated estimation error of dimendependent density ratio So E g (pL... tpt (x,) - w', (xx |l3]dt is only 39.1%. compared to
+ [|| //2- (xo) - w& (x))]/])ce We additionally discuss the benefits of time-dependent discriminator training in Appendix A.2 The natural way to reduce this DRE error is to employ time- dependent importance reweighting based on the time-dependent density ratio, as this paper suggests for the first time in the line of work on diffusion models.
Jo IE (m Pan))
3.2 SCORE MATCHING WITH TIME-DEPENDENT IMPORTANCE REWEIGHTING
The objective LISM utilizes the samples from the joint space of p(xg, X1), so applying time- dependent importance reweighting is not straightforward. We start with LsM. which entails expec- tations marginal distribution. We apply time-dependent importance reweighting through eq. (9).
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13
1.0
0.5
2
2
0.0
(a) log Pairs (X)
(b) log Pasta (xo)
V log ui (xo)
(d) u (25))
Figure 3: (a-b) The score plots on Pas and plat defined in Figure 2 (c) The score plot score cor-
rection term. (d) The reweighting value. The time-dependent density ratio simultancously mitigates
the bias through (c) and (d).
/ Eptu (xx) w/y- (0, xi) dt,
(f: Pdlta)
where (0, = X(t) (s)))ss((xx))))))) (x(;
V log Pamm (s))l. and u (xx)
Piee (x:1) Plise (xc))
Meanwhile, this objective is still intractable because we cannot evaluate V log Paam (x,) from sam- ple Xg. Also, there is mismatching between the sampling distribution Plizs (xx) ) and the density func- tion of target score V log Plata (x.). This difference interferes with the straightforward conversion to a denoising score-matching approach.
To tackle this issue, we propose an objective function named time-dependent importance reweighted denoising score-matching (TTW-DSM). There exists a new score correction term, log w (xt)
(xm( as a regularization in the L2 loss on score-matching. v log (x,)
LTIWEDSM O: Phins; w (.))
(10)
2 2 (xo) (x(x)/xa) A(t)wrg (xt) (x,,) - V log p(x/ V log w (xx) [3]] dt
Here, we briefly explore the meaning of the newly suggested regularization term through
V log w/ (x,) = V log Plnta (xx) V log Poias (x,)
V log w/ (x,) forces the model scores to move away from V log logpltss (x,) and head towards
V log Pana (x:). Figure 3 interprets this score correction scheme on the 2-D distributions as de- scribed Figures 2 and 2b FigureBaa Salshows that V log Poian (x:) incorporates a substantial portion of the mode in the lower left. The correction term in Figure 3c exerts force away from the biased mode, allowing
model target the V log Plana( (xx) as shown Figure 3b) Figure 3d illustrates the reweighting values, which assigns small values the points from the biased mode, and imposes larger weights on the points from another mode. The time-dependent density ratio simultancously mitigates the bias through score correction and reweighting.
Moving beyond the conceptual explanations, the following theorem guarantees the mathematical validity of the proposed objective function.
Theorem 1. LIIW-DSM (i; Pbiar; w/y- (-)) LS Pdiaa) + C, where C is constant W.E. O.
See Appendix A.I for the proof. We declare that the proposed objective function equivalent to the classical score- matre-na objective with Pdata Despite the equivalence, implementing only LDSM with Drr for our problem not viable option due the limited amount of Dæzr from Pdata- LDSM will suffer from Monte Carlo approximation error from limited data (See Appendix C for more details). In contrast, our objective allows for the use of biased data Doias which has many more data points. Furthermore, the following corollary guarantees the optimality of the proposed objective.
Corollary 2. Let 0 Diw-DDMM arg ming LTIW-DM (0; Pbias w/y (-)) be the optimal parameter. Then 80 (x,, 1) V log V' (x,) for all xt, l.
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While we utilize biased datasets, the equivalence of the objective functions ensures the proper op- timality. We also incorporate utilizing of Dett for practical implementation (See Appendix (..4) In summary, converge model distribution to the underlying true unbiased data distribution by utilizing all observed data.
4 EXPERIMENTS
This section empirically validates that the proposed method effectively operates on real-world biased datasets. We outline the experiment setups below.
Datasets We consider CIFAR-10, CIFAR- 100, FFHQ. and CelebA datasets, which are commonly used for generative learning. Note that we access the latent bias factor only for the data construction and evaluations. To construct Drins we consider class as latent bias factor CIFAR-10 and CIFAR-100. For human face datasets, gender and hair color for CelebA. To construct Dict. we randomly sample a subset from the entire unbiased dataset. We experiment with various numbers of [Pret] on each dataset. See Appendix D.1 for more detailed explanations of the dataset.
consider gender as latent bias factor for FFHQ, and both
Metric Our goal is to make the model distribution converge unbiased distribution. To measure this, we use the Fréchet Inception Distance (FID) (Heusel et al. (017). which measures the distance between the distributions. We calculate the FID between 50k samples from the model distribution and 2) all the samples from the entire unbiased dataset.
Baselines We establish three baselines for main comparison. DSM(ref) and DSM(obs) denote the naive training diffusion model with Dier and Dobs, respectively. IW-DSM denotes a method using time-independent importance reweighting in eq. 77). and TIW-DSM denotes our method in eq. (1O). Note that both IW-DSM and TIW-DSM also incorporate the use of DDer for our experiment (See Appendix A.4 for more details), and we always use the same experimental setting across the baselines by only varying objective functions (See Appendix D.2 for the detailed training configu- rations).
4.1 LATENT BIAS ON THE CLASS
Table I: Experimental results on CIFAR-10 and CIFAR-100 datasets with various reference size. [Par]] The reference size indicates [Dai.l All the reported values are the FID (І) between the generated
samples from each method and all the samples from the entire unbiased dataset.
Data
Bias set
CIFAR-10 (LT)
CIFAR- 100 (LT)
Reference size
5%
10%
25%
50%
5%
10%
25%
50%
DSM(ref))
16.47
11.56
10.77
5.19
21.27
17.17
15.84
8.57
Method
DSM(obs)
12.99
10.75
8.45
7.35
15.20
11.06
8.36
6.17
IW-DSM
15.79
11.45
8.19
4.28
20.44
15.87
12.81
8.40
TIW-DSM
11.51
8.08
5.59
4.06
14.46
10.02
7.98
5.89
35
30
DSMIrel
WSD
25
(a) DSM(ref) (16.47 / 06
(b) IW-DSM (15.79/ 0.18)
(c) DSM(abs) (12.99 0.42)
(d) TIW-DSM (11.51 / 0.40)
(e) Training Curve
Figure 4: Analysis on CIFAR- 10 (LT / 5%) experiments. (a-d) Samples that reflect the diversity and latent statistics with (FID/ Recall). (e) Training curves for each method.

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We construct Dias following the Long Tail (LT) dataset (Cao al. 2019) for CIFAR- 10 and CIFAR- 100. Table shows the results with various reference sizes. First all, the performance gets better as the reference size gets larger for all methods. Secondly, when comparing DSM(ref) and DSM()bs), we find that the naive use of Drias yields better results when the reference size is too small, or the strength of bias is weak (case of CIFAR-100). However, DSM(obs) exhibits poor performance when the reference size becomes larger in the CIFAR-I0 dataset. Since DSM(obs) does not guarantee converge on the unbiased distribution, the performance also not guaranteed under such an extreme bias setting. Third, IW-DSM consistently exhibits slightly better performance compared DSM(ref), IW-DSM utilizes Diet as well as Doias with the weighted value. However, we observed that the reweighting value for Daias is too small (will be discussed in section[.44) which makes the effect of the Driss marginal. In many cases, the performance of IW-DSM is even worse than the naive use of Driss- Finally, the proposed method TIW-DSM outperforms all the baseline models in every case we tested by a large margin. The comparison of IW-DSM and TIW-DSM directly indicates the effect of dime-dependent importance reweighting. IW-DSM and TIW-DSM optimize two equivalent objective functions up to a constant under optimal density ratio functions (See Appendix A..3 for explanation), the performance gain is purely from the accurate estimation of the time-dependent density ratio.
Figure 4 shows the samples in (a)-(d) and the convergence curve on each method in (e). DSM(ref) and IW-DSM illustrate extremely low sample diversity, which results in many samples being iden- tical. DSM(obs) displayed variety of samples, but it is heavily biased. Out of 10 latent classes, latent classes accounted for 40% of the total proportion that is being calculated by a pre-trained clas- sifier. TIW-DSM shows the diverse samples with unbiased proportions. We provide quantitative measure of bias intensity in Figure 7 Additionally, Figure 4e shows that DSM(ref) and IW-DSM suffer from overfitting, which often occurs when training with limited data (See Appendix C for explanation). This could be evidence that IW-DSM cannot fully utilize the information from Drias-
4.2 LATENT BIAS ON SENSITIVE ATTRIBUTES
Table 2: Experimental results on FFHQ with various bias settings
20
80%
& reference size. The reference size indicates reported values are the FID (L).
[Dal
All the
80% 5%
[
90%
14
90%/12.5%
Data
Bias set
FFH (80%)
FFHQ (90%)
Reference size
1.25%
12.5%
1.25%
12.5%
DSM(ref)
12.69
6.22
12.69
6.22
10k
20k
30k
40k
Method
DSM(obs)
7.29
4.88
8.59
5.75
Figure 5: The convergence of TIW-DSM on various bias level & reference size.
Training Progress (5mgg
IW-DSM
11.30
5.50
11.68
5.60
TIW-DSM
7.10
4.49
8.06
4.83
(a) FFHQ (Gender 90% / 1.25%)
(b) CelebA (Benchmark/ / 5%)
Figure 6: Majority to minority conversion through our objective. The first row illustrates the samples from DSM())s), and the second row illustrates the samples from TIW-DSM under the same random seeds. (a) indicates the female to male conversion. (b) indicates the (female & non-black hair) to (male& black hair) conversion.
We construct Dbins by making the portion of females as 80% and 90% in FFHQ experiments. Ta- ble 2 demonstrates the performance on each bias setting and various reference sizes. TIW-DSM shows superior results similar to the results from Table I This experiment includes scenario with an extremely small reference set size, which is 1.25%. TIW-DSM still works well on very lim- ited reference sizes. While TIW-DSM aims to estimate the unbiased data distribution regardless
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of the intensity of bias in Diiss lower bias intensity led to better adherence to the unbiased data distribution. providess the stable training curves for various experiment settings.
We also tackle the bias that actually exists in the common benchmark. We observe CelebA benchmark has suffered from bias with respect to gender and hair color. we consider four subgroups: female without black hair (RF,NR), , male without black hair (2M.NB). female with black hair (2g,)), and male with black hair (2M.B), each group has the following proportion: p(2r nB² 46.5%. pl (M,NB) = 29.6%. p(2r,n) 11.5%. (M..B)(M)))))
Table 3: Mitigating the bias exists in the CelebA
benchmark dataset with 5% reference size.
Latent Statistics (%)
Method
FID
2F,NB
2M,NB
2F,B
DSM(ref) DSM(obs)
2.82
28.0
29.8
19.3
22.9
3.55
42.8
30.0
13.0
14.2
IW-DSM
2.43
34.6
29.7
17.1
18.6
TIW-DSM
2.40
31.0
27.8
20.1
21.1
12.4%. We construct the (Diell as 5% of CelebA datasets, which random samples from the unbiased dataset. Table shows the experiment results for the CelebA dataset. To examine the effectiveness of weak supervi- sion itself, we train DSM(obs) without using the information of Per in this experiment, which shows poor results from bias. TIW-DSM also outperforms the other baselines in terms FID, implying that it is the best approach address real-world bias under weak supervision. Additionally, examine the latent statistics on generated samples using pre-trained classifier (See Appendix [D.3 for details). Figure [bb shows the generated samples from the proposed method that reflects such proportions. Figure explicitly shows the reason why the bias was mitigated. Some of the sam- ples looked in the majority latent group from DSM(obs) transformed into minority group from TIW-DSM. These changes helped to adjust toward the equal portion in each subgroup.
4.3 ABLATION STUDIES
Loss component The proposed loss function utilizes the time-dependent density ratio for two purposes, which is the reweighting (W) and the score correction (C). We conduct ablation stud- ies in Table assess the effectiveness of each role. Note that if we do not use both, the objec- tive becomes the same as DSM(obs). Using only reweighting without score correction does not guarantee that the model distribution will con- verge to an unbiased data distribution, so the per- formance does not improve. While using only score correction establishes missing link to the traditional score-matching objective, it ensures that the model converges to an unbiased data dis- tribution (See Appendix AA.5 for mathematical explanation), which showed quite good results. The use of these two components simultaneously performs best in most cases.
Table Component ablation on the pro- posed method. W indicates the time-dependent reweighting term, indicates the score correc- tion term. All reported values are FID (4).
Component
Reference size
W
C
5%
10%
25%
50%
X
X
12.99
10.57
8.45
7.35
X
13.27
10.80
8.26
7.28
X
11.62
8.15
5.43
4.14
11.51
8.08
5.59
4.06
0.325
0.25
DSW)jsf)
0.34
DSM(ja)) D6M(bb)
0.300
DSM(bba)
0.275
TWWDSMM
IM-DBM
0.32
0.25
IN-DGM
TWWDSM
0.250
9.20
0.125
= 0.25
0.200
0:175
2.5
0.150
15
16
20
21
FD
FID
(a) CIFAR-10 10 (LT 5%)
(b) CIFAR-100 (LT 5%)
Figure 7: Bias FID tradeoff's on the methods. We sweep a E (0.25, 0.5, 1, 2.5) for TIW-DSM, and a E {0.125, 0.5, 0.25, 1} for IW-DSM.
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Density ratio scaling The density ratio confidence of the classifier can be scaled through hyperparameter after training (Dhariwal& & Nichol 2021). We generalize our objective utilizzing the a-scaled density ratio: LTWWDSM function and a 0 becomes equivalent to DSM() which is explained in Appendix[A.6 We con- sider the experiments on CIFAR- 10 and CIFAR- 100 with a 5% reference set size. We also conduct scaling on the IW-DSM baseline. For quantitative analyses, we also measure the strength of bias through Bias == Σg Ex. [p(2|x) Ex (p(2|x)]ll (See Appendix D.3 for more detail about this metric). Figure| 7 Jillustrates that DSM(ref) shows poor FID because only trains
DSM Pbiass Pbias: " (+)% Note that
indicates the original objective
small amount of Drer while being free from the bias. DSM(obs) achieves better FID from a larger amount of data but suffers from bias. IW-DSM almost linearly trade-off these two metries by adjusting a. TIW-DSM showed improvements in both metrics within the alpha range of 0 to 1. Furthermore, TIW-DSM outperforms IW-DSM significantly in terms of FID at the same bias strength.
4.4 DENSITY RATIO ANALYSIS
40k
#f Samples (blos)
30K
female
male
20k
~ Densty
10K
feraal make
10
10"
10
10"
10"
10"
10"
10"
10'
10"
Reweighting Value vQ(kc)
Reweighting Value wgix)
Heweighting Value wg(x))
Reweighting Value wg(x))
(a) (f) 0
(b) ott) = 0.34
(c) (+)) 0.72
(d) (+))) 80
Figure 8: Reweighting value analysis on Doias and Dier of FFHQ (Gender 80% / 12.5%) according to diffusion time (t). (a) Most of the reweighting value Doias is extremely small. (d) Most of the reweighting value is on both Dria. and Dret- (b-c) smooth interpolation between (a) and (c).
This section investigates the importance reweighting value ac- cording to the diffusion time in our experiment. Figure 8 illuss- trates the histrogram of reweighting values on Driu in FFHQ (Gender 80% 12.5%). When the diffusion time (t) 0, the trained discriminator predicts overconfidently, resulting in more than 75% of Drias being assigned weights less than 0.01.
Sewelpingg mg0m)
x!
x
Since IW-DSM only uses the weight value on (() = 0, it
does not utilize most of the information from Dotas. This is the reason why the performance of IW-DSM is only marginally better than DSM(ref). While the perturbation undergoes, the reweighting value grows rapidly, which TIW-DSM leads to utilizing more information from Doias- Note that the minor- ity latent group (or, the males in this setting) tends get higher value of reweighting value than the major group (fe- male group) in each diffusion time step, which is the reason for bias mitigation. Figure 9 shows point-wise examples that
10'
Partatzaaan State
x(1
Figure 9: The density ratio changes according to the diffusion time.
change the importance weights in Drias- x2)) and (3) have extremely low reweighting values o(t) O, but these weights increase as time progresses, pro- viding valuable information for TIW-DSM training.
5 CONCULSION
In this paper, we address the problem of dataset bias for the diffusion models. We highlight the previous iime-independent importance reweighting undergoes error propagation from density ratio estimation, and the proposed time-dependent importance reweighting alleviates such problems. We derive the proposed weighting objective to become tractable by utilizing the time-dependent den- sity ratio for reweighting as well as score correction. The proposed objective is connected to the traditional score-matching objective with unbiased distribution, which guarantees convergence to an unbiased distribution. Our experimental results on various kinds of datasets, weak supervision settings, and bias settings validate the proposed method's notable benefits.
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ACKNOWLEDGMENTS
This research was supported by AI Technology Development for Commonsense Extraction, Reason- ing, and Inference from Heterogeneous Data([ITP) funded by the Ministry of Science and ICT(2022- 0-00077).
REFERENCES
Tameem Adel, Isabel Valera, Zoubin Ghahramani, and Adrian Weller. One-network adversarial fairness. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 33, pp. 2412- 2420, 2019.
Brian DO Anderson. Reverse-time diffusion equation models. Stochastic Processes and their Ap- plications, 12(3):313-326, 1982.
Jyoti Aneja, Alex Schwing, Jan Kautz, and Arash Vahdat. Nep-vae: Variational autoencoders with noise contrastive priors. 2020.
Martin Arjovsky and Leon Bottou. Towards principled methods for training generative adversarial networks. In International Conference on Learning Representations, 2017.
Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale gan training for high fidelity natural image synthesis. International Conference on Learning Representations, 2018
Kaidi Cao, Colin Wei, Adrien Gaidon, Nikos Arechiga, and Tengyu Ma. Learning imbalanced datasets with aabel-distribution-www margin loss. Advances in neural information processing systems, 32, 2019.
Junyi Chai and Xiaoqian Wang. Fairness with adaptive weights. In International Conference on Machine Learning, pp. 2853-2866 PMLR, 2022.
Kristy Choi, Aditya Grover, Trisha Singh, Rui Shu, and Stefano Ermon. Fair generative modeling via weak supervision. In International Conference on Machine Learning, pp. 1887-1898 1898. PMLR, 2020.
Prafulla Dhariwal and Alexander Nichol. Diffusion models beat gans image synthesis. Advances in neural information processing systems, 34:8780-877 87794, 2021.
Rahul Duggal, Scott Freitas, Sunny Dhamnani, Duen Horng Chau, and Jimeng Sun. Har: hardness aware reweighting for imbalanced datasets. In 202/ IEEE International Conference on Big Data (Big Data), pp. 735-745, IEEE, 2021.
Cynthia Dwork, Moritz Hardt, Toniann Pitassi, Omer Reingold, and Richard Zemel. Fairness through awareness. In Proceedings of the 3rd innovations in theoretical computer science confer- ence, pp. 214-226, 2012.
Michael Feldman, Sorelle A Friedler, John Moeller, Carlos Scheidegger, and Suresh Venkatasubra- manian. Certifying and removing disparate impact. In proceedings of the 21th ACM SIGKDD international conference on knowledge discovery and data mining, pp. 259-268, 2015.
Eric Frankel and Edward Vendrow. Fair generation through prior modification. In 32nd Conference on Neural Information Processing Systems (NeurIPS 2018), 2020.
Felix Friedrich, Patrick Schramowski, Manuel Brack, Lukas Struppek, Dominik Hintersdorf, Sasha Luccioni, and Kristian Kersting. Fair diffusion: Instructing text-to-image generation models on faimesss. arXiv preprint 2xxv:2332..0089) 2023.
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farke Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. Advances in neural information processing systems, 27, 2014.
Alexandros Graikos, Nikolay Malkin, Nebojsa Jojic, and Dimitris Samaras. Diffusion models as plug-and-pla. priors. Advances in Neural Information Processing Systems, 35:14715-14728, 2022.
10

---

Published as a conference paper at ICLR 2024
Dandan Guo, Zhuo Li, He Zhao, Mingyuan Zhou, Hongyuan Zha, et al. Learning re-weight examples with optimal transport for imbalanced classification. Advances in Neural Information Processing Systems, 35:25517-25530, 2022.
Michael Gutmann and Aapo Hyvärinen. Noise-contrasee contrastive estimation: new estimation principle for unnormalized statistical models. In Proceedings of the thirteenth international conference artificial intelligence and statistics, pp. 297-304. JMLR Workshop and Conference Proceedings, 2010.
Melissa Hall, Laurens van der Maaten, Laura Gustafson, Maxwell Jones, and Aaron Adcock. A systematic study of bias amplification. arXiv preprint arXiv:2201. //706, 2022.
Moritz Hardt, Eric Price, and Nati Srebro. Equality of opportunity in supervised learning, Advances in neural information processing systems, 29, 2016.
Hoda Heidari, Claudio Ferrari, Krishna Gummadi, and Andreas Krause. Fairness behind a veil of ignorance: A welfare analysis for automated decision making. Advances in neural information processing systems, 31, 2018.
Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to local nash equilibrium. Advances in neural information processing systems, 30, 2017.
Jonathan Ho and Tim Salimans. Classifier-free diffuusion guidance. In NewrlPS 2021 Workshop on Deep Generative Models and Downstream Applications, 2021.
Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33:6840-6851, 2020.
Zhihao Hu, Yiran Xu, and Xinmei Tian, Adaptive priority reweighing for generalizing fairness improvement. In 2023 International Joint Conference Neural Networks (IJCNN) pp. 01-08. IEEE, 2023.
Ben Hutchinson and Margaret Mitchell. 50 years of test (un) fairness: Lessons for machine learning. In Proceedings of the conference on fairness, accountability, and transparency, pp. 49-58, 2019.
Vasileios losifidis and Eirini Ntoutsi. Adafair: Cumulative fairness adaptive boosting. In Proceed- ings of the 28th ACM international conference on information and knowledge management, pp- 781-790, 2019.
Tero Karras, Samuli Laine, and Timo Aila. A style-based generator architecture for generative adversarial networks. In Proceedings the IEEE/CVF conference computer vision and pattern recognition, pp. 4401-4410, 2019.
Tero Karras, Miia Aittala, Janne Hellsten, Samuli Laine, Jaakko Lehtinen, and Timo Aila. Training generative adversarial networks with limited data. Advances neural information processing systems, 33: 2104-121141, 2020.
Tero Karras, Miika Aittala, Timo Aila, and Samuli Laine. Elucidating the design space of diffusion- based generative models. Advances in Neural Information Processing Systems, 35:26565-26577, 2022.
Dongjun Kim, Seungjae Shin, Kyungwoo Song, Wanmo Kang, and I1-Chul Moon. Soft truncation: A universal training technique of score-based diffusion model for high precision score estimation. In The 39th International Conference Machine Learning, ICML 2022. International Confer- ence on Machine Learning, 2022a.
Dongjun Kim, Yeongmin Kim, Se Jung Kwon, Wanmo Kang, and Il-Chul Moon. Refining genera- tive process with discriminator guidance in score-based diffusion models. In Andreas Krause, Emma Brunskill. Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett (eds.), Proceedings of the 40th International Conference on Machine Learning. volume 202 of Proceedings of Machine Learning Research, pp. 16567-16598. PMLR, 23-29 Jul 2023.

---

Published as a conference paper at ICLR 2024
Yeongmin Kim, Dongjun Kim, HyeonMin Lee, and chul Moon. Unsupervised controllable gen- eration with score- based diffusion models: Disentangled latent code guidance. In NeurIPS 2022 Workshop Score-Based Methods, 2022b.
Emmanouil Krasanakis, Eleftherios Spyromitros Spyromitros-xooufis, Symeon Papadopoulos, and Yiannis Kom- patsiaris. Adaptive sensitive reweighting to mitigate bias in fairness-aware classification. In Pro- ceedings of the 2018 world wide web conference, pp. 853-862, 2018.
Alex Krizhevsky. Learning multiple layers of features from tiny images. Technical report, 2009.
Chieh-Hsin Lai, Yuhta Takida, Naoki Murata, Toshimitsu Uesaka, Yuki Mitsufuji, and Stefano Er- mon. Fp-diffusion: Improving score-based diffusion models by enforcing the underlying score fokker-planck equation. 2023.
Tongliang Liu and Dacheng Tao. Classification with noisy labels by importance reweighting. JEEE Transactions pattern analysis and machine intelligence, 38(3):447-461, 2015.
Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang. Deep learning face attributes in the wild. In Proceedings of International Conference on Computer Vision (ICCV), December 2015.
Christos Louizos, Kevin Swersky, Yujia Li, Max Welling, and Richard Zemel. The variational fair autoencoder. arXiv preprint 151 1.00830, 2015.
Cheng Lu, Kaiwen Zheng, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu. Maximum likelihood training for score- based diffuuson odes by high order denoising score matching. In International Conference Machine Learning, pp. 14429-14460. PMLR, 2022.
Vittorio Maggio. The bias problem: Stable diffuusio, 2022. URL URL medi um cttp::/hheebbis--pppooeeee-aaeaa wwwbblllddiffufsee www.ffoooooooeeeeeeeeee-00- 2022.
Chenlin Meng, Yutong He, Yang Song, Jiaming Song, Jiajun Wu, Jun- Zhu, and Stefano Ermon.
Sdedit: Guided image synthesis and editing with stochastic differential equations. In International Conference on Learning Representations, 2021.
Tachong Moon, Moonscok Choi, Gayoung Lee, Jung-Wer Woo Ha, and Juho Lee. Fine-tuning diffusion models with limited data. In NeurIPS 2022 Workshop
Score-Basee Methods, 2022.
Byeonghu Na. Yeongmin Kim, HeeSun Bae, Jung Hyun Lee, Se Jung Kwon, Wanmo Kang, and Il chul Moon. Label-noise robust diffusion models. In The Twelfth International Conference on Learning Representations, 2024.
Alexander Quinn Nichol and Prafulla Dhariwal. Improved denoising diffusion probabilistic models. In International Conference on Machine Learning, pp. 8162-8171. PMLR, 2021.
Alexander Quinn Nichol, Prafulla Dhariwal, Aditya Ramesh, Pranav Shyam, Pamela Mishkin, Bob Mcgrew, Ilya Sutskever, and Mark Chen. Glide: Towards photorealistic image generation and editing with text-guided diffusion models. In International Conference on Machine Learning, pp- 16784-16804. PMLR, 2022.
Sebastian Nowozin, Botond Cseke, and Ryota Tomioka. f-gan: using variational divergence minimization. Advances in neural information processing systems, 29, 2016.
Training generative neural samplers
Seulki Park, Jongin Lim, Younghan Jeon, and Jin Young Choi. Influence-balanced loss for im- balanced visual classification. In Proceedings of the IEFF/CVF International Conference on Computer Vision, pp. 735-744 2021.
2021.
Mengye Ren, Wenyuan Zeng, Bin Yang, and Raquel Urtasun. Learning to reweight examples for robust deep learning. In International conference on machine learning, pp. 1334-4343. PMLR, 2018.
Benjamin Rhodes, Kai Xu, and Michael U Gutmann. Telescoping density-ratio estimation. Ad- vances in neural information processing systems, 13:4905-4916 2020.
12

---

Published as a conference paper at ICLR 2024
Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Bjöm Ommer. High- resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF confer- on computer vision and pattern recognition, pp. 10684-10695, 2022.
Kevin Roth, Aurelien Lucchi, Sebastian Nowozin, and Thomas Hofmann. Stabilizing training of generative adversarial networks through regularization. Advances in neural information process- ing systems, 30, 2017.
Nataniel Ruiz, Yuanzhen Li, Varun Jampani, Yacl Pritch, Michael Rubinstein, and Kfir Aberman. Dreambooth: Fine tuning text-to-image diffusion models for subject-driven generation. In Pro- ceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 22500- 22510, 2023.
Prasanna Sattigeri, Samuel C Hoffman, Vijil Chenthamarakshan, and Kush R Varshney. Fairness gan: Generating datasets with fairness properties using a generative adversarial network. IBM Journal of Research and Development, 2019.
Jiaming Song. Pratyusha Kalluri, Aditya Grover, Shengjia Zhao, and Stefano Ermon. Learning controllable fair representations. In The 22nd International Conference on Artificial Intelligence and Statistics, pp. 2173. PMLR, 2019.
Jiaming Song, Qinsheng Zhang, Hongxu Yin, Morteza Mardani, Ming- Yu Liu, Jan Kautz, Yongxin Chen, and Arash Vahdat. Loss-guided diffusion models for plug-and-play controllable generation. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett (eds.), Proceedings of the 40th International Conference on Machine Learning, volume 202 of Proceedings of Machine Learning Research, pp. 32483-32498. PMLR, 23-29 Jul 2023.
Yang Song and Stefano Ermon. Generative modeling by estimating gradients of the data distribution. Advances in neural information processing systems, 32, 2019.
Yang Song and Stefano Ermon. Improved techniques for training score-based generative models. Advances in neural information processing systems, 33: 13:11248-12444 2020.
Yang Song and Diederik P Kingma. How to train your energy-basee models. arXiv preprint 21X:v:2101.03288, 2021.
Yang Song, Jascha Sohl-Dickstein, Diederik Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. In Interna- tional Conference on Learning Representations, 2020.
Yang Song, Conor Durkan, lain Murray, and Stefano Ermon. Maximum likelihood training of score- based diffusion models. Advances in Neural Information Processing Systems, 14:1885-1428, 2021.
Masashi Sugiyama, Taiji Suzuki, and Takafumi Kanamori. Density ratio estimation in machine learning. Cambridge University Press, 2012.
Christopher TH Teo, Milad Abdollahzadeh, and Ngai-Man Cheung. Fair generative models via transfer learning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pp. 2429-2437, 2023.
Tatiana Tommasi, Novi Patricia, Barbara Caputo, and Tinne Tuytelaars. deeper look at dataset bias. Domain adaptation in computer vision upplications, pp. 37-55, 2017.
Antonio Torralba and Alexei A Efros. Unbiased look at dataset bias. In CVPR 2011, pp. 1521-1528. IEEE, 2011.
Masatoshi Uchara, Issci Sato, Masahiro Suzuki, Kotaro Nakayama, and Yutaka Matsuo, Generative adversarial nets from density ratio estimation perspective. arXiv preprint arXiv:1610.02920, 2016.
Soobin Um and Changho Sub. fair generative model using lecam divergence. In Proceedings of the AAAI Conference Artificial Intelligence, volume 37, pp. 10034-10042, 2023.
13

---

Published as a conference paper at ICLR 2024
Pascal Vincent. A connection between matching and denoising autoencoders. Neural compu- tation, 23(7):1661-1644, 2011.
Ruxin Wang, Tongliang Liu, and Dacheng Tao. Multiclass learning with partially corrupted labels.
IEEE transactions on neural networks and learning systems, (966)2558-2580) 2017a.
Yingheng Wang, Yair Schiff, Aaron Gokaslan, Weishen Pan, Fei Wang. Christopher De Sa, and Volodymyr Kuleshov. InfoDiffusion: Representation learning using information maximizing dif- fusion models. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett (eds.), Proceedings of the 40th International Conference Ma- chine Learning, volume 202 of Proceedings of Machine Learning Research, pp. 36336-36354. PMLR. 23-29 Jul 2023a.
Yu-Xiong Wang. Deva Ramanan, and Martial Hebert. Learning model the tail. Advances in neural information processing systems, 30, 2017b.
Zhendong Wang, Huangjie Zheng, Pengcheng He, Weizhu Chen, and Mingyuan Zhou. Diffusion- GAN: Training GANs with diffusion. In The Eleventh International Conference on Learning Representations, 2023b.
Zhisheng Xiao and Tian Han. Adaptive multi-stage density ratio estimation for learning latent space energy-based model. Advances Neural Information Processing Systems, 35:21590-21601, 2022.
Zhisheng Xiao, Karsten Kreis, and Arash Vahdat. Tackling the generative learning trilemma with denoising diffusion GANs. In International Conference on Learning Representations, 2022.
Depeng Xu, Shuhan Yuan, Lu Zhang, and Xintao Wu. Fairgan: Fairness-awaee generative adver- sarial networks. In 2018 IEEE International Conference on Big Data (Big Data), pp. 570-575. IEEE, 2018.
Yilun Xu, Shangyuan Tong, and Tommi S. Jaakkola. Stable target field for reduced variance score estimation in diffusion models. In The Eleventh International Conference on Learning Represen- fations, 2023.
Rich Zemel, Yu Wu, Kevin Swersky, Toni Pitassi, and Cynthia Dwork. Learning fair representations. In International conference on machine learning, pp. 325-333. PMLR, 2013.
Min Zhao, Fan Bao, Chongxuan Li, and Jun Zhu. Egsde: Unpaired image-to-image translation via energy-guided stochastic differential equations. Advances in Neural Information Processing Systems, 35:3609-3623, 2022.
Huangjie Zheng, Pengcheng He, Weizhu Chen, and Mingyuan Zhou. Truncated diffusion prob- abilistic models and diffusion-based adversarial auto-encoders. In The Eleventh International Conference on Learning Representations, 2023a.
Kaiwen Zheng, Cheng Lu, Jianfei Chen, and Jun Zhu. Improved techniques for maximum likelihood estimation for diffusion ODEs. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett (eds.), Proceedings of the 40th International Conference on Machine Learning, volume 202 of Proceedings of Machine Learning Research, pp. 42363-42389, PMLR, 23-29 Jul 2023b.
Linqi Zhou, Aaron Lou, Samar Khanna, and Stefano Ermon. Denoising diffusion bridge models. In The Twelfth International Conference Learning Representations, 2024.
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CONTENTS
Introduction
2
Background
2.1
Problem Setup
2.2
Diffusion model and score matching
2.3
Density ratio estimation
2.4
Importance reweighting for unbiased generative learning
3
Method
3.1
Why time-dependent importance reweighting?
3.2
Score matching with time-dependent importance reweighting
Experiments
Latent Bias on the class
2
Latent bias sensitive attributes
4.3
Ablation Studies
Density ratio analysis
Conculsion
Proofs and mathematical explanations
17
A.
Proof of Theorem]] []
17
A.2
Theoretical analysis on time dependenn discriminator training.
19
A.3
Relation between time- indeenndeendden importance reweighting and time time-deeemeee dependent im-
portance reweighting
20
A.4
Objective for incorporating Diet
20
A.5
Loss component ablations).
A.6
Generalized objective function by adjusting density ratio
21
Related work
23
Fairness in ML & generative modeling
23
B.2
Importance reweighting
23
Score correction in diffusion model
24
B.4
Time-dependent density ratio in GANs
24
Overlitting with limited data
24
D Implementation detail
25
D.1 Datsets
25
D.2 Training configuration
26
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D.3 Metric
27
D.4 Algorithm
27
D.5 Computational cost
28
Additional experimental result
28
E.1
Comparison GAN baselines
28
Trainig curve
28
Sample comparison
................................
29
Density ratio analysis
29
E.5
Effects of discriminator accuracy
36
E.6
Comparison to the guidance method
37
E.7
7
Objective function interpolation
38
Fine tuning Stable Diffusion
F,9
Data augmentation with Stable Diffusion
40
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A PROOFS AND MATHEMATICAL EXPLANATIONS
A.1 PROOF OF THEOREM 1
Pdaaa) Theorem 1. CIIW-DSM (0; Phiar: w (-)) = Lsse( Pdada)) + C, where C' is constant w.r.l. O.
Proof. First, the score-matching objective LSM(O; Pddat) can be derived as follows.
/'"
Ls Pdata)
/
Exiin (xx)
w (xx smm (mm))x((0 dt
(12)
/.
/ Enga (xx)
w (xx)){()(ss0(xx) t) V log Patta (x, 11 dt
(13)
Enin (x6)
w (xx) t)ll 2V log Pdata (x) )² (xe,
V log Pdan (x 112] df (14)
We further derive the inner product term in the above equation using eq.
Eppi (xx)
V log Petnaa (xx) so (xx:
(15)
= Poius (xx)
V log Poins (xx) + log us- (xx))* so (xe, t) dx;
(16)
Jdxs |xx, / Phias (xx)
Pilus (xx)
V llogPria Prias (x.) sx 1)
V Flog war (x,) so (xe, 1) dxe (17)
We obtain the derivation for the first term of eq.
17 using the log derivative trick.
I Proun (xx) V Vlgg Phias (x:)²* "sol (xex f)dx
(18)
/ Phiss (xx) so'sss "xx,,x t)dx;
(19)
/ Poias (Xo) (x: X ]dxo] f (xx, t)dx;
(20)
f! |t Poias (xo) Vroc (x, X )dxp] " "so (x(, t)dx,
(21)
I Prius Xp Vpne (x, (x) so (x,, f)dx
(22)
/ ʃ Phim Poe) (x log Por (x,|Xo) (xo) J so t)dx,
(23)
15 pxpc (xo) Soor (xo)
V log poe (x. xo) X so so t))
(24)
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Applying eqs. (17) and 24 eq. 14 we have:
CsM(O (0; Pamaa)
(25)
1
//²
(xi) w/s (xx) (xx 2V log Pdata (x1) 3s0 (x(x t)
= 2
+ V log Pdata (x:)11
dt
(26)
1
2.
Ppma(xo) Eoos (xel(())) xx)
w/ (x)))(t([lsso(x t)11 - 2V log Puata (x,) ) " (x t)
dt + C1
2
(27)
1
2/
T
Bynu xo) poo xo) w/g- (x)))((t((lss(xxx.)))))) t)1l 2V Pou sx dt
Expa E (x01x00
us (x,) (x,, Ci (2w (xx) log
(28)
2
1
T
(xn (xpttxrixo) xx) w/a- (xx)))(0)[(ss(xxx.))) V Pog di C2
2
1
1'" Exsi ) Poe (x)) (2w's (x,)A(t)Vil log w (x, (x, +
(29)
2
1
('
(x))(xx)) (p(xx))o)) A(t)as (xx) se (xx, t) v log xo)1
2
2s0 (x:. 1) v w (xt) dt + C1+02
(30)
1
/
Exii(xx)) (xp(x)eo))
s(t)erk (xx) (x)][[ss (xe, 1) V log xo)
2
250 (x,, 1) log wt (xx) + 2V log p( xo) log w (xt)
+ || V log why 1 dt + + + C2
(31)
- /'" (xo) (xo) Ex(x)exo) (xo) X(t)cs (ss V (ogp((x(xx)) V log whe (x:)11 dt + C
1
(32)
=CrIW-DMM(P) Poias; w +C
(33)
where C₁, C2, C3, be constants that do not depend on O. Thus, LTWWDSM (0; Priass w (.)
equivalent to LsM (0; Pdaaa) with respect to
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A.2 THEORETICAL ANALYSIS ON TIME-DEPENDENT DISCRIMINATOR TRAINING.
We further discuss the training objective of time-dependent discriminator in eq. (34). We inves- tigate whether optimizing at each time step of the density ratio would have beneficial impact other times. Theorem | provides some indirect answer. The minimization of log ratio estimation error guarantees the smaller upper bound of the estimation error at 0 for a point.
CT-ECE(0r Pdata: Poias) := 1/" ((tt (xx) (x.))logoooooooo (x t)] + Byg (xx, [log(1 dx(x,, t))
(34)
Theorem 3.
Suppose the model density ratio w and Pine are continuously differentiable on their Plus
Paa is nonzero at any [0, 1]", then we have Vina
supports with respect to t, for any x. Assume
log w (x) - log Pedma (x)
log wos (x) - log Péina (x)
+ +C(xx, () 0(t))
Plias (x)
Pilas (x)
where C(x, 4: Φ))
1 log w (x)
0 log Plu (xc)
For any 0, set कf
or
Ples [x]
arg ming B(c,(+e) [R (xx) log do ()] + F. Pi (xx) log (1 dx(xx, [))]] Then, the following
properties hold:
log w/y (x) = log Pano (x) Plan (x))
C(xx t; (,)) = O.
for any Therefore, optimal 6i, the following inequality holds:
Pednto (x)
log wag (x) - log
S S0((3).
p (x)
Proof. From the Taylor expansion with respect to variable, we have
Pú (x)
Piasa (x)
log w/d(x) - log
log w' (x) - loog
Plsas (x)
Potas (x)
t 0
② log
Pálna (x) pluss (x)
log (x))
+ 0(t))
0t
Ot
which derives
Pdata (x)
Placa (x)
log w (x) llog
< log wx) log
+0(xx, (t) 0(t)),
Plins (x)
Prins (x)
by triangle inequality. Now, if Φb = arg min Ble,ete) [E (x,) logg de (x1, t)] (x..) log (1 - dx(xi, t))]].
then w (x) = doy (x.
(x)(x) for any x and a E [t, t + e). Therefore, we get
I-do; (xx,0]
Pa
Pluea (x)
log w/ w/ (x) log
0
Phice (x)
by plugging / to Also, get
i 01.
log 2 (x)
log wi 25
(xx()
log w/;
(x)
lim u x
log Pri (x)
Pim (x)
log Pdu, (xc) Plece (x)
lim
u "
log Piuta (x)
Ot
Phins (x))
since (x) Pii (x)
is continuously differentiable with respect to t. Therefore, C(x, t; Φ?) 0.
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A.3 RELATION BETWEEN TIME-INDEPENDENT IMPORTANCE REWEIGHTING AND DEEE-DEPNNDENT IMPORTANCE REWEIGHTING
This section explains further equivalence between the objective functions of IW-DSM and TIW- DSM. We rewrite the objective function of time-independent importance reweighting as follows:
LIW.DSM (0; Phins, w (-))
(35)
(x) was (x0) (xa) X(1) (x))((x)1)) V log (x)op { dt,
2
where we- (x6) := Paaul LIW Poizs ug- (.)) is equivalent to LUSM (0: Paaaa) as de- (
rived in eq. 66 and eq. We also know the equivalence between LIwWDDM (f; Peius: wz- (-))
Since LSM pdam) and LDSM Patata) are equiva- lent (Song & Ermon 2019). we conclude that the objectives LIW.DSM (0; Pbias: us- (-)) and CTIW-DSM O Poias W (-)) are equivalent w.r.t. & up to a constant.
and LsM( (0; Praat from Theorem
This equivalence implies the empirical performance between IW-DSM and TIW-DSM is purely from the error propagation from the estimated time-independent density ratio w () and the time- dependent density ratio (t).
A.4 OBJECTIVE FOR INCORPORATING DDRFF
The objective functions of TIW-DSM and IW-DSM in the main paper explain how to treat Diias for unbiased diffusion model training, but we actually have Pobs Diet Drins. The objective that incorporates Der is necessary for better performance of the implementation.
To do this, we define the mixture distribution Pétss :- ti P and plug P into phiss in each objective. Note that the density ratio between Pinu and Póus also can be represented by the time-dependent discriminator we explained in the main paper.
(x+)
ii pi (x+)
Pits (x()
2Prnn (xx) + Di (xx)
2 (Xe+)
(Ke)
2 (x..)
2w/h (xx)
Marn (Xe))
--da (xe,1)
2d
2x1, (xt,
(36)
+ Eli (Xe.)
1 w (xx)
da- (Xx.t)
+
Plas (xe)
(xx,1)
By plugging Pots and ii into objective function, can get the objective function that incor- porates all the samples in Dobs-
LIWWDDM (0: Pobs; 1i/0 (-))
(37)
= 2 2 Exp (xo) (p(xx1x0o ((t)ūg (xx [Ise t) V pxx:/xx)Xo) - V log uh (x,) [3)] dt
In the same spirit, the time-independent importance reweighting objective that incorporates Dref represented as follows:
LIW-DSM (0; Pobs: Pobs: No (-))
(38)
1
Bput (20 (xo) xx)) (()o(ls)( V log pxx, Xx) [13)] dt,
2
where Te- (Xo)
2 (xa) Pas (xa)
The DSM(obs) in experiment optimize the following objective in eq.
39
1 [."
LDSM (0: Pats) -
(xod( (xx) Exp(xe (xo)
[Iseel)) - V log Plogp(xx/x))133 de (39)
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A.5 LOSS COMPONENT ABLATIONS
The proposed objective function, eq. (40), utilizes wh as two roles in our method: 1) reweighting and 2) score correction. We discuss what if each component did not exist.
LTIW-DSM (0: Poias w/z(() (-))
(40)
E (x.) (x,)) Bp(xx|xo) (x03
x(t)ugg (xse)(())))) V logp(xx(xo)) V log w (xx))BB) de
J
First, consider the objective function that only takes the score correction:
2 I
Eru (Mo) Bpxx (x0)
(xo
A(t) (xx,) Vlogp(x( - V log w (xx) dt.
(41)
If we define newly parameterized distribution sig (xx, == se (x t) log w (xt) as the model distribution (the adjusting parameter is still only 0), the objective becomes like eq. (42)
1 I Pxpe (xpxelxx)) (()[(1)(((x.)) V 1ogp((;/xo)lB3)) di
(42)
2
This objective is same as CDSM with Poias. so s/g(X,, f) will converge to V log Pbias (xx). By the re- lation from So (x,, 1) s (x,, V Vlog w (x,). (x(x,,)) will converges log Prias (x,) +
log Pdata (xx). This means that only applying score correction guarantees opti- mality, so this the reason for the quite good performance.
V log (x,) Prud X+)
Second, we consider the objective function that only takes the time-dependent reweighting:
1 1./ (x (x(x)))))
2
A(t)ur (x,) [||s t)
pl dt.
(43)
We can derive that eq. 443 is equivalent to following objective in eq. 44
2 J
E (x.)
A(t)w (xx) |xoe, t) V log Peins (xx) |13)]
dt.
(44)
which implies that Sy (xe, () will converge to V log Poias (x,). This is the reason that the objective
without score correction performs similarly to DSM(obs).
A.6 GENERALIZED OBJECTIVE FUNCTION BY ADJUSTING DENSITY RATIO
We generalize objective for the ablation study in Section 4.3 by adjusting the density ratio, which represented as eq. (45)
CTIW-DSM (0; Poias / (-)9)
(45)
1 1/10 Exaa (xn) Epix, xxo) = 2
A(1)/g- (xx) [1lso(xx.))
[xlss () - logp(x:(xo) a log w (x:)
As 0. C.W.DSM (0; Poias w/z- (-) becomes LosM (0; Phias) i.c..
LIIW-DSM Poias w/g (-19)
(46)
Epnac Bp(x.(bo)) [(t)([so(xe)))) (x),))) V log log X
(xx) [[3)] dt LDSM O Prias)
2 J
To adopt this scaling to our objective with incorporate Diet. we utilize the relation in eq. 447 and define ui (x,, a:) through eq. (48)
2w (xx)
To te (xx) = + w (xx)
(47)
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2w' (x))
w (xx, a) + w//- (xx)
(48)
Then, the a-generalized objective that incorporates Pett can be expressed as follows.
CIIW-DSM (0; pobs; u (:)
(49)
A(t)ūg (x,, [I]se(x,,, t) V ((gg((x()x)) - V log ui (x,, a}][a]] df
= 2 0 (xx)) /p(xe (xo)
As + 0, wi (x,, a)) becomes 1, which leads V log te (x1, (.) be 0.
CIW-DDM ( Pobs, 2 ())
20 Exn (ptx, (oo)
1
>(1))'s (xe, (x((ss((x(,))) V Vlogp(x:(xo) log wy (xr. 0).:0)1 [)] dt
/'" Exoo (xx) (x)
{(1)[1s5((x:1)) 1) Vlogp(x/xx)183)) xx)] de
2
LO:sM(O:oot)
(50)
This implies that a interpolates the objective function between DSM(obs) and TIW-DSM. We can observe the quantitative results also interpolated the range of E [0, 1] as shown in Figure 7
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B RELATED WORK
B.1 FAIRNESS IN MI. & GENERATIVE MODELING
Fairness is widely studied in the fields of classification tasks (Dwork et al.; 2012 Feldman et al. 2015
Heidari et al. 2018 Adel et al.) 2019), representation learning (Zemel et al. [013] Louizos
2015: Song et al. 2019 ) and generative modeling (Um Suh 2023] Sattigeri et al.) 2019] Xu et al.) 2018 8 Teo et al. 2023). In terms of classification tasks, the objective for fairness is mainly to handle a classifier to be independent the sensitive attributes such as gender with different mea- surement metries (Hardt et al.) 2016 Feldman al. 2015). Fair representation learning is defined as equal representation which is a uniform distribution of samples with respect to the sensitive at- tributes (Hutchinson & Mitchell 2019).
al.
The task we address in this paper is also called fair generative modeling (Xu et al. 2018 Choi et al., 2020 Teo et al., 2023), which aims estimate a balanced distribution of samples with respect to sensitive attributes. With regard to data generation, there are relevant works such as Fair-GAN (Xu et al. 2018) and FairnessGAN (Sattigeri al. 2019). These methods have been advanced to gener- ate data instances characterized by fairness attributes, with their respective labels. These generated data instances are utilized as a preprocessing step. On the other hand, Teo et al. (2023) introduces transfer learning to learn a fair generative model. They adapt the pre-trained generative model trained by large, biased datasets via leveraging the small, unbiased reference dataset to finefune the model. Choi et al. (2020); [Um & Suhj (2023) treat fair generative modeling under weak supervi- sion setting so utilize the small amount of reference dataset. Most of the fair generative models have progressed using GANs. In the diffusion models, we propose, that the concept relevant to fairness & dataset bias has not yet received significant attention.
Friedrich et al. 2023 is concurrent study that explores the theme of fairness in diffusion models, but their work is distinctly differentiated from our paper in terms of problem setting and methodol- ogy. Our paper focuses on weak supervision setting, which is a cost-effective scenario in terms of dataset collection. Conversely, |Friedrich et al. (202)) leverage information in the joint space of (text, image) using pre-trained text conditional diffusion model. This implies that their approach relies on point-wise text supervision to mitigate bias. There is also a distinguishable difference in the methods. |Friedrich et al. (2023) is based on the guidance method, which requires 3 times more NFEs for sampling. Our paper proposes the objective function for unbiased score network training, so we only need NFE of score network at every denoising step. Please refer Appendix E.6 for quantitative comparison.
B.2 IMPORTANCE REWEIGHTING
There are many approaches to rewcighting data points for their purpose, which is common in the fields of noisy label learning (Luu & Tao 2015 Wang et al. (0177)), class imbalanced learning (Ren let al. 2018 Guo et al. 2022 Duggal et al. 2021 Park et al. 22021) and faimess (Chai & Wang 2022
Hu et al. 2023 Krasanakis al. 2018 Iosifidis & Ntoutsi 2019). In the context of learn- ing with noisy labels, importance reweighting aims to adjust the loss function by assigning reduced weights instances with noisy labels and elevated weights to instances with clean labels, thereby mitigating the impact of noisy labels on the learning process Liu & Tao 2015). Similar to the con- cept from the noisy label, research from class imbalanced learning utilizes an importance reweight- ing scheme to prevent the model from being biased to the majority classes while amplifying the effects of minority classes (Wang al. 2017b; Ren et | 2018 Guo et al. 2022). In terms of fair- ness, there are researches for importance reweighting (Chai & Wang 2022 Hu et al.) 2023). These works on fairness aim to mitigate representation bias which is caused by insufficient and imbalanced data instances in fair perspective. Consequently, they propose instance reweighting means to facilitate fair representation learning within the model.
The reweighting related to time t is considered in diffusion models (Nichol & Dhariwal 2021 Song jet al.] 202T Kim et al. 2002a).. However, these studies focus on resampling and reweighting the random variable /. itself, while we focus on the reweighting xt-
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B.3 SCORE CORRECTION IN DIFFUSION MODEL
The sampling process of the diffusion model involves an iterative update process using a score direc- tion, typically approximated by the score network. When there is specific purpose for generating data, score correction becomes necessary. There are several methods to adjust this score direction, each tailored to specific purposes, From technical standpoint, these methods can be divided into two groups: guidance methods and score-matching regularization methods.
Guidance methods introduce additional gradient signals to adjust the update direction. Classifier guidance (Song et al.) 2020) Dhariwal & Nichol, 202T) utilizes a gradient signal from a classifier to generate samples that satisly condition. Classifier-free guidance (Ho & Salimans) 2021 also aims at conditional generation but relies on both unconditional and conditional scores. Furthermore, various methods have been proposed to enable controllable generation using auxiliary models with a pre- mre-trained unconditional score model (Graikos et al. 20222 [Sng et al. (002)) On the other hand, discriminator guidance (Kim et al.] 2023) serves a different purpose by enhancing the sampling performance of a diffusion model through the use of a discriminator that distinguishes between real images and generated images. EGSDE (Zhao al., 2022) leverages guidance signals based on energy functions, enhancing unpaired image-to-image translation. Guidance methods have the advantage of utilizing pre-trained score networks without the need for additional training. However, they require separate network training for guidance and additional network evaluation during the sampling process.
There is body of work on score marteeig regularization for better likelihood estimation (Lu et al., 2022 Zheng et al., al.,|222222 2023b Lai et al., 2023). Na et al. (2024) propose a regularized conditional score- matching objective to mitigate label noise. The unique benefit of score-matching regularization is that it does not require an additional network at the inference stage.
B.4 TIME-DEPENDENT DENSITY RATIO IN GANS
Density ratio closely associated with the training of GANs (Goodfellow et al. 2014, Nowozin al. 2016 Uehara et al. (0166). The discrimination between perturbed real data and perturbed gen- crated data is often mentioned in GAN literature. This is because the discriminator of a GAN also suffers from a density-chasm problem, and a noise injection trick could resolve it. Arjovsky & Bot- tou (2017) propose method to perturb real data and fake data with a small gaussian noise scale for discriminator input, but the practical choice of noise scale in high-dimension is not easy (Roth al., 2017]. Wang et al. (2023b) propose multi-scale noise injection using a forward diffusion process and introduced adaptive diffusion technique, achieving significant performance improvements in nigh-dimensional datasets. Xiao et al. (2022;; Zheng et al. (023a) utilize GAN's generator to achieve fast sampling in the reverse diffusion process, and they also naturally conduct discrimination between perturbed distribution. However, the dime-dependent discriminator in GANs fundamentally differs in its use case from the proposed method that serves the roles of reweighting and score cor- rection.
C OVERFITTING WITH LIMITED DATA
We observe the FID overfitting phenomenon when we train diffusion models with too small a subset of data. In GANs, the origin of overfitting is well elucidated by Karras et al. (2020). However, in diffusion models, the origin of overfitting is not well explored but often reported from the litera- ture (Nichol & Dhariwal 2021: Moon et al. 2022 Song & Ermon 2020). Training configurations, such as network architecture, EMA, and diffusion noise scheduling, affect this phenomenon. One thing explicitly observed from Figure iO is that overfitting becomes serious when the number of data becomes smaller. Our experiment sometimes considers a small amount of data, so we periodically measure the FID and choose the best one.
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40
500
16
1000
30
10000
12
25
20000
20
15
20k
40k
60k
80k
100k
0
10000 20000 30000
40000
50000
Training Progress (Kimg)
Number of training data
(a) Training curve various numbers of data
(h) FID under various # of data with early stopping
Figure 10: Overfitting in FID with a limited number of training data in training diffusion model with CIFAR-10.
D IMPLEMENTATION DETAIL
D.1 DATSETS
We explain the details of the dataset construction for experiment. about Doius Drer and the entire unbiased dataset. To construct Diiss we define the bias statistics in each latent subgroup (See Figure [ for the proportion), and randomly sampled from each subgroup. Once we established Dias. we conducted experiments using the same set for all baselines. The ground truth bias information each data point is provided from the official dataset in CIFAR- 10, CIFAR-100, and CelebA. We use bias information for FFHQ from https: /tttttbb..bt/.t//g com/ DCGM/ featu--featteee---ee aste The entire unbiased dataset is used construct Dret and evaluation. We set the entire unbiased dataset as almost the maximum number of samples that are balanced under latent statistics. The reference dataset Drer is randomly sampled from the entire unbiased dataset. Note that we do not intentionally balance the latent statistics in Diers and we use the same Dier for all baselines.
the information
Table Dataset configurations
CIFAR-10
CIFAR-100 100
HPHQ
CelebA
Resolution
3 x 32 32
3 32 x 32
64 61
3 x 61 x 6-1
Bias dataset Dia
Number of instances
10000 10
10000
40000
162770
Hair color) (2. 2)
Bins subgroup
100
2
Bias type
Long tail
Long tail
80%, 9U%
Benchmark
Entire unbiased dataset
Number
Number of instances in each bius group
5000
500
25000
18784
Reference dataset Dar
Number of insiances
500, 1000, 2500, 5000
500, 2500, 5000
500, 5000
8140
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0000
500
805
3002
2
Number
2000
200
100
Laleni
(a) CIFAR-10 (L.T)
(b) CIFAR-100 (I.T)
(c) CelehA (henchmark)
Figure 11: The latent statistics in each Diiss
D.2 TRAINING CONFIGURATION
We follow the procedures outlined in EDM (Karras et al. 2022) to implement the diffusion mod- els only by changing the learning batch size and objective functions. For the time-dependent discriminator, we follow DG (Kim al. 2023). Table 0 presents the details of our experi- ment. We utilize the model architecture, and training configuration of diffusion model from com/ NVI abs/edsm For CIFAR-10 and CIFAR- 100 experiments, we fol- low the best setting that is used for 10 in EDM. For FFHQ and CelebA experiments, follow the best setting that used for FFHQ in EDM, except for batch size. For time-dependent discriminator, utilize the setting from time-dependent discriminator consists of two U-Net encoder architectures. We use a pre-trained U-Net encoder from ADM https: //ts::///iiii titbbbtt..... com/ owweaooe////ooooooo qud-ddddddddd f fus on which is as a feature extractor. We train the shallow U-Net encoder that transforms from the feature to the logit. For sampling, utilize EDM deterministic sampler. To implement limeeindependent dis- criminator for IW-DSM, we utilize the same discriminator architecture but only feed-forward t = for time inputs.
https://githut
com/ aaaaaaaaduue alw.aassduurrrr 10
The
Table 6: Training and sampling configurations.
CIBAR-10
CIFAR-100
FEHQ
CelebA
Scure Network Architeclure
Rackbone
DDPM+
DDPM
Channel multiplicr
128
128
128
128
Channel per resolution
2-2-2
2-2-2
1-2-2-2
1-2-2-2
Score Network Training
Learning rate x 10
10
10
2
2
Augment probubility
12%
12%
15%
15%
Dropout probubility
13%.
13%:
5%
5%
Batch size
256
256
128
128
Discriminator Architecture
Feature extractor
Backbone
encoder
U-Net encoder
U-Net encoder 2
U-Net encoder
depth
2
width
128
128
128
128
Attention Resolations
32,16.
32,16, 8 128
32,16, 8 128
32,16, 8
Discriminator Training
Batch size
128 VP Importance
128 Cosine VP Importance
Perturatton
VP
Cosine VP Importance
Time sampling
Importance
Learning rate x10
Iteration
10k
10k
10k
10k
Sampling
Solver type
ODE
ODE
ODE
ODE 79
Solver order
2
NPF.
35
35
79
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D.3 METRIC
FID measures the distance between the sample distributions. Each group of samples is projected into the pre-trained features space and approximated through Gaussian distribution. So, FID measures both sample fidelity and diversity. We consider this to be the metric to indicate how well the model distribution approximates an unbiased data distribution. We utilize https://githui com/ NVlabs/ edm for FID computation.
For the analysis purpose, use the metrics recall. The recall describes how well the generated samples in the feature space cover the manifold of unbiased data. We utilize this metric to highlight the reason why IW-DSM shows so poor FID performance in We utilize httpp::/gggiie com/ chen/ hao chao / al sm for recall computation.
Bias (Choi et al. 2020) is also utilized for the analysis. This metric measures how similar la- tent statistics are to the reference data. This metric requires pre-trained classifier Pe that distin- guishes the latent subgroups. The classifier trained on the entire unbiased dataset. We use pre- trained vgg/3-bn model from htt / thub. com/ hwtp///pwaa/yyoooro.pppaptap CIFARI for CIFAR-10, pre-trained DenseNer-BC (L= /90, k=40) from http::ttpps...mm /ttg:///itth com haaam//baaaa///// for CIFAR- 100. This latent classifier is also used to compute the portion of the latent group for sample visualization. For FFHQ and CelebA, we utilize our discrim- inator architecture with only feed-forward / 0, and adjust the output channels.
Bias Mg | [p(z|x) Ex-~p [p(2/x)]ll>
(51)
D.4 ALGORITHM
Algorithm 1: Discriminator Training algorithm
Input: Reference data Dres biased data Diices perturbation kernel Prjo. temporal weights Output: Discriminator dæ
while not converged do
Sample X1 ......,.pp XB/2 from Dier
Sample Xg/2+1:-.. XB from Dris
Sample time [1, 1p/2, LB/2+1 Lg from [0,
Diffuse x ,..., 8B/2, -B/241;-., x using transition kernel Pejo
1 1 B/2 ((4) log (x;, (4) Ei-//21 A(t.) log(1 dø (x:: 4:))
Update & by using the gradient descent method
end
Algorithm 2: Score Training algorithm with TIW-DSM
Input: Observed data Das. discriminator Φ" perturbation kernel Peju: temporal weights À Output: Score network se while not converged do
Sample from D.... and time i from [0, 7]
Sample from the transition kernel P:jo
Evaluate ú (xx) using eq. (66)
I + A(t) b (xx)
(ko]lsss [sp (X,, t) V log p(x; (xb) log wig- (xx)
Update by using the gradient descent method
end
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D.5 COMPUTATIONAL COST
In this section, we compare the TIW-DSM and IW-DSM regarding computational costs. Both meth- ods require the evaluation of the discriminator during the training phase, but the evaluation proce- dures are somewhat different. IW-DSM only requires the feed-forward value of the discriminator. On the other hand, TIW-DSM requires the value V log w (-). which necessitates auto gradient op- eration in PyTorch. This slightly increases both training time and memory usage. Once the training is complete, the discriminator is not used for sampling, so the sampling time and memory remain the same. Table showws the computational costs measured using RTX 4090 x 4 cores in the CIFAR-10 experiments. Note that the training time- ameedeeendent discriminator is negligibly cheap, converging around 10 minutes with RTX 4090.
Table 7: The computational cost comparison between IW-DSM and TIW-DSM.
IW-DSM
TIW-DSM
Training time
0.26 Second Batch
0.34 Second / Batch
Training memory
13,258 MiB x Core
15,031 MiB x 4 Core
Sampling time
7.5 Minute / 50k
7.5 Minute / 50k
Sampling memory
4,928 MiB x 4 Core
4,928 MiB x 4 Core
E ADDITIONAL EXPERIMENTAL RESULT E. COMPARISON TO GAN BASELINES
The reason we developed a methodology with a focus on the diffusion model is because it demon- strates superior sample quality compared to other generative models like GANs. To validate this, we conducted experiments with a GAN baselines. Table g compare the performance with GAN. GAN(ref) and GAN(obs) indicates the GAN training with Diet and Dots. repectively. IW-GAN is applying importance reweighting on GAN training (Choi et al. 2020). We observed train- ing GAN with limited data resulted in failure, which is often discussed in the literatures (Karras) et al. 2020). IW-GAN also exhibited similar phenomenon, as it hardly utilized the informa- tion from Doias as discussed in Section 4.4 The issue with limited data actually led better performance when we used all the observed data. Due to these issues, the quantitative metrics did not perform well, so we removed them from our considerations. We utilize the code from https: / github.. wtt.//////eeeeeee wmwngroopu.pooooooo wuipo/ir////aggnnnnnn/ fairgen. and modify the resolution for CIFAR-10. Figure shows the samples from GANs.
Table 8: Comparision to GAN baselines on CIFAR-10 (LT) experiment. The reported value is FII) (L).
Reference size
5%
10%
25%
50%
GAN(ref)
284.11
246.75
144.32
56.29
GAN(obs)
42.09
36.45
35,67
34.42
IW-GAN
260.32
235.22
120.23
50.32
IW-DSM
15.79
11.45
8.19
4.28
TIW-DSM
11.51
8.08
5.59
4.06
E.2 TRAINIG CURVE
We provide more training curves on CIFAR- 10 and CIFAR-100 experiments. We measured the FID in increments of 2.5K images during the early stages of training and then in increments of 10K images after reaching 20K images for all our experiments. See Figure 13 for training curves, which demonstrate the training stability of TIW-DSM.
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(a) IW-GAN (5%)
(b) IW-GAN (10%)
C IW-GAN (25%)
(d) IW-GAN (50%)
(e) GAN((bs) (5%)
(I) GAN(obs) (10%)
(g) GAN(obs) (25%)
(h) GAN(obs) (50%)
Figure 12: Samples from GAN baselines according to the method and reference sizes.
43
CSMine IN-35M
25
0000
NN-3S TIWDDSM
20
TIW-DSM
DSMject
15
20k
40%
BEK
804
120k
20k 42k
B0k
80
100k
20k
42h
604
83k
100K
204 40%
60X
80k
100k
Tranning Progress (0mg)
Traniing Progress (0mg))
Training Frogress (k0mg)
Trahnnng Progress (K0m))
(a) CIFAR-I0 (LT. 5%)
CIFAR 100 (LT, 5%)
(c) CIFAR- (LT, 50%)
(d) CIFAR -100 (LT, 50%)
Figure 13: Training curves CIFAR-I0/ CIFAR-100 experiments.
E.3 SAMPLE COMPARISON
We further provide the samples from each experiment in Figures 15 18 portion of each latent group on samples through Appendix D.3 and reflect the latent statistics on each generated sample. Figure [4]swoss more examples that the conversion from majority group to minority group through the proposed method in CelebA experiment.
We examine the pro-
(a) (male bon-black hair) to (male& black hair)
(b) (female non- bon-black hair) to (female& black hair)
Figure 14: Majority to minority conversion through objective in CelebA (Benchmark, 5%) experiment. The first row illustrates the samples from DSM(obs), and the second row illustrates the samples from TIW-DSM under the same random seed.
E.4 DENSITY RATIO ANALYSIS
We provide more density ratio statistics according diffusion time in various experiments which are discussed Section 4.4 Figures 2o 23 shows the case FFHQ, and CelebA. Appendix E.4 shows the reweighting value the 2-D cases.
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(a) DSM(
(h) IW-DSM
(c) DSM(obs)
(d) TIW-DSM
Figure 15: Samples that reflect latent statisties from CIFAR-10 (LTT / 5%) experiment.
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(a) DSM(ref)
(b) IW-DSM
(c) (Sb()
(d) TIW-DSM
Figure 16: Samples that reflect latent statistics from CelebA (Benchmark, 5%) experiment
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DSM(ref)
(b) DSM
(c) DSM(abs)
(d) TIW-DSM
Figure 17: Samples that reflect latent statisties from FFHQ (Gender 80%, 1.25%) experiment
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(a) FFHQ (Gender 90%, 1.25%
(b) FFHQ (Gender 90%, 12.5%)
(c) FFHQ (Gender 80%, 1.25%)
(d) FFHQ (Gender 80%, 12.5%)
Figure 18: Samples that reflect latent statistics from TIW-DSM according bias strength & refer- ence size in FFHQ experiments.
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62
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Figure 20: Density ratio analysis on FFHQ (Gender 80%, 12.5%) on various diffusion time for Dbias
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Figure 21: Density ratio analysis on FFHQ (Gender 90%, 12.5%) on various diffusion time for Drius
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Namber of Stampi Stmplee
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Figure 22: Density ratio analysis on CelebA (Benchmark, 5%) on various diffusion times. This figure only consider female in Drins-
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Figure 23: Density ratio analysis on CelebA (Benchmark, 5%) on various diffusion times. This figure only consider male in D
a Sameten Baia)
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Figure 24: Density ratio analysis FFHQ (Gender 80%, 12.5%) zero diffusion time with ratio scaling for Doias (box plot) and Derr (density plot).
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E.5
EFFECTS OF DISCRIMINATOR ACCURACY
0.7
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(c) Discriminator accuracy according to the time
(d) FID according to discriminator learning progress
Figure 25: Effects of discriminator accuracy on diffusion model training in CIFAR-10 (LT 5%) experiments. The maturity of the time-dependent discriminator directly influences the performance of the diffusion model.
We analyze the learning progress of the time-dependent discriminator and its correlation with the diffusion model's performance. Figures 25a and 25b show the time-integrated accuracy and time- integrated loss value according the discriminator training iteration. Note that perfect discrimina- tion terms of accuracy impossible at a large perturbation scale. Figure 25c shows the accuracy according to (t). As the training of time-dependent discriminator matures, accuracy improves for all perturbation scales.
Our objective, LTwWDSM (0: (0; Phias; w/y (+)) assumes optimal time-dependent discriminator, anal- ysis maturity of the discriminator is important. Figure 25d shows the performance when training TIW-DSM using a less-trained discriminator. In the very early stages, the discriminator provides signals that are completely off, resulting in worse performance compared to DSM(obs). However, as it undergoes some level of training, it progressively enhances the performance of the diffusion model. The time-dependent discriminator with 1. 1.5k iterations shows FID of 11.52, which is nearly close to the reported value in the Table of 1 11.51 obtained with 10k iterations. Note that the training 10k iterations of the discriminator only takes 30 minutes with RTX 4090.
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E.6 COMPARISON TO THE GUIDANCE METHOD
direct quantitative comparison with Friedrich et al. (023) is infeasible because their approach is based a weak supervision setting. However, their method is based on the commonly used guidance method in the diffusion model, and it is possible to adapt the spirit of that method to our weak supervision scenario.
The unbiased data score V log Pdata (x,) can be represented by eq. (52). and it can be approximated with neural networks for better performance. This is similar mechanism in Section 4.3) Density ratio scaling. Table P and Figure 26] compare the guidance method and proposed method by adjusting a. Note that the
eq. (53). a for an ideal scenario, but it is usually adjusted
guidance method requires the evaluation of 2 neural networks for one denoising step, resulting in slow sampling.
Prius (Xe)s(Xe))
V log Pattta (x4) V log Pbius (X4)
log Pdata (X()
(52)
d (xx,, t)
~ so(e, () + aV log
(53)
dæ (X,,
Table 9: The comparison between the guidance method (Fair-Difflusion and TIW-DSM for CIFAR- 10 (LT 5%) experiments.
DSM(obs)
TIW-DSM
FID 1)
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Figure 26: Comparison guidance method (Fair-Diffusion by adjusting for CIFAR-10 (LT /5%) experiments.
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E.7 OBJECTIVE FUNCTION INTERPOLATION
The time-dependent density ratio used in TIW-DSM is more precise than the time-independent den- sity ratio, in the integration accurate for small diffusion time. One attractive direction is utilizing vanilla objective LDsM Poins) for small diffusion time. Small diffusion time is known to be oriented towards denoising rather than addressing semantic information (Rombach et is worth exploring.
However, the time-marginal density ratio from w (-) remains in-
2022
Xu
2023), so objective interpolation
We experimented with the preliminary approach, which interpolates the objectives as eq. 54 Note that ar (r) O indicates the original TIW-DSM objective, and a(T) = 80 indicates the vanilla DSM objective.
Interppoatee (0; Phins w ())
(54)
(x Ex(xx (xc))
A(1) [11s0(xe;)) () V Vlogp(xx/xo0033))
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A(t)wá (x:) t) Vlogp(x,1xo) - V llog wi (xx))1 dt
2 Exa Bxxx (x(x)xx)
Contrary to intuition, the result in Figure 27 shows that it does not improve the performance but rather smoothly interpolates between objectives. We suspect that a hard truncation between the objectives may not be the best choice. We consider the gradual change of the objective according to time future work.
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Figure 27: Objective interpolation according to (T) in CIFAR-10 (LT 5%) experiments.
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E.8 FINE TUNING STABLE DIFFUSION
The existing large-scale text-to-image diffusion model suffers from serious bias (Maggio 2022 For example, if you type "nurse" in the prompt, only female nurses appear, as shown in Figure 28 Our method involves mitigating latent bias, so we can consider a scenario where we mitigate gender as latent bias. We obtained reference dataset of approximately 50 images and fine-tuned Stable Diffusion (Rombach et al. 2022) for the "nurse" prompt using the framework in Ruiz et al. (2023) with our objective TIW-DSM, The fine-tuned Stable Diffusion successfully generated male nurse as shown in Figure 29
We consider this to be the primary result applying our objective to rext-to-image diffusion mod- els. In addition to fine-tuning, this approach can be applied to training text-to-image model from scratch. Constructing a reference set for (prompt, bias) pairs deemed important by society and ap- plying objective during training, should enable relatively fair generation.
NIMTUC CAR1
NUSIM
NITEE
PRUI e
Narn
NALAR NLRNE
NETS
Figure 28: Samples from Stable Diffusion with prompt "nurse"
Figure 29: Samples from fine-tuned Stable Diffusion on prompt "nurse" with TIW-DSM.
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E.9 DATA AUGMENTATION WITH STABLE DIFFUSION
The baseline (SM(r does not exhibit good performance, because it suffers from a limited number of Drer leading poor diversity of generated samples. One consideration to request Stable Diffusion to generate unbiased samples and use them in conjunction with Dret- We request Stable Diffusion to generate 500 samples with the prompt "a photo of man" and another 500 samples with the prompt "a photo of woman" and resizing them to fit our experiment setting in FFHQ as shown
in Figures 30 and 31
Figure 30: Samples from Stable Diffusion with prompt "a photo of man"
Figure 31: Samples from Stable Diffusion with prompt "a photo of woman"
Table 10 presents indirect results quantifying the data augmentation method using Stable Diffusion. The method SD represents the performance of directly generated samples from Stable Diffusion. It's noteworthy that SD exhibits poor performance 95.63, primarily because unannotated biases such as age, and race are not controlled. On the other hand, DSM(ref) and TIW-DSM utilize statistics from balanced reference data, which is free from unannotated bias without point-wise supervision. This result underscores the reason why we should not rely solely on a large-scale foundation model. DSM(ref) + SD indicates the half of generated samples from DSM(ref) and the other half of the samples from SD. This can be considered as a performance similar to vanilla DSM training with Drer and generated samples from SD. The performance of DSM(ref)+SD is poor due serious bias in Stable Diffusion samples.
Table 10: The effects of data augmentation with Stable Diffusion for FFHQ (80% / 12.5%) experi- ments.
Method
FID 50k
FID lk
DSM(ref)
6.22
21.87
SD
95.63
DSM(ref) + SD
43.57
TIW-DSM
4.49
20.39
40


Reviews:
[{"review_id": "KkNN5wMCuW", "reviewer": "Reviewer_EYEW", "summary": "The paper proposes a time-dependent importance-sampling objective for diffusion models, to mitigate the bias in the training set. The idea is to estimate the time-dependent importance weights between the bias distribution and the true (unbiased) distribution. The importance-weighted score-matching objective is then translated into a corresponding denoising score-matching objective. Controlled experiments showcase the effectiveness of the proposed method.", "questions": "- For the experiments, do the authors generate 50k images to calculate the FID score? What's the architecture and noisy schedule used in this paper? The current FID score seems quite worse off.\n\n- How can this method be used in practical text-to-image generation?", "limitations": "", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- The paper proposes a new denoising score-matching objective to tackle the biases in the training set.\n\n- In contrast to the previous method (Eq.7), the proposed method estimates the time-dependent density ratio, which is arguably easier to estimate.\n\n- Experiments on CIFAR-10/CIFAR-100/FFHQ demonstrate that the proposed method (TIW-DSM) not only outperforms baselines with solely reference unbiased data but also beats the vanilla go-to method IW-DSM.", "weaknesses": "- The biggest concern I have is that the proposed methods lack practical significance, and seem tangent to practical settings. The biases problem studies in this paper go away when considering conditional generation (e.g., text-to-image generation). For example, we can generate a batch of male images by conditioning on the \"male\" label, even though the female images are the majority. \n\n\n- Regarding comparison to baseline (IW-DSM), some of the claimed advantages are not rigorous：(1) On page 4, \"the perturbation provides an infinite number of samples from each distribution.\": note that the perturbed distribution is $p_{data} * N(0, \\sigma_t^2)$, one would still need large amount of data in $p_{data}$ (or $D_{ref}$) in order to estimate quantities related to $p_{data} * N(0, \\sigma_t^2)$. (2) It's true that the accumulated MSE error in the density ratio estimation is smaller in the proposed method, but it introduces an additional erroneous term $\\nabla \\log w$ in the new objective. It could result in an even larger error compared to the baseline.\n\n- Fig. 8.(a): I think a better density ratio estimator can get away from this over-confidence issue. A simple method is to regularize the classifier such that it cannot perfectly distinguish the two distributions.\n\n\n- A natural baseline missing in the paper is asking generative models (e.g. SDXL) to generate more unbiased data for the considered small datasets and train the model in the vanilla DSM way.\n\n## Update\n\nI would like to thank the authors for the new experiments. The experiments showcase some promising results on applying the debiasing techniques to Stable Diffusion. However, one could argue that the chosen mode is too large (i.e., nurse). If the input prompt is \"male nurse\", then the problem still goes away without any fine-tuning. In addition, I could not immediately see why introducing the erroneous term $\\nabla \\log w$ would not negatively affect the training.\n\nI raised my score to 5 based on the new experiments.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "4AyrnThbdg", "reviewer": "Reviewer_6Mt9", "summary": "The paper proposes time-dependent importance reweighting to mitigate the dataset bias for diffusion training. The proposed method utilizes time-dependent density ratio estimation, which is more precise than the previous time-independent one used in GAN. The authors provide both theoretical understanding and empirical demonstrations of the proposed method's benefits.", "questions": "1. I can see the arguments for time-dependent density ratio estimation the same as the ones for [1] (especially), [2], etc. Thus I suggest the authors make the citations and discussions accordingly. Nonetheless, I agree that the use case of DRE is different.\n2. In theory, the method works if $E_{x_0 \\sim p_{\\textrm{bias}}(x_0|x_t)} [\\nabla\\log p(x_t|x_0)] = \\nabla\\log p_{\\textrm{bias}}^t(x_t)$ and DRE's gradient actually contains $\\nabla\\log p_{\\textrm{data}}^t(x_t)$ information. Both require DRE to be really accurate, which, as the authors demonstrate, is reasonably true only for large $t$. Thus, might I suggest that the authors only train with Eq.10 for large $t$, and revert back (gradually) to standard diffusion training on the biased dataset for small $t$? The intuition is that for small $t$, the model only does denoising, which does not care about dataset biases (the model has already decided on the content it wants to generate). For an intuitive understanding, see Fig.2 in [3]. For a more theoretical explanation see [4], where small $t$'s score field is dominated by one sample, making the score for unbiased the same as biased here.\n3. In Fig.4, every method's performance peaks early and gets worse. This is unexpected for me. Could the authors provide an explanation?\n\n\n[1] Wang et al. \"Diffusion-gan: Training gans with diffusion.\" ICLR 2023.\n\n[2] Arjovsky et al. \"Towards principled methods for training generative adversarial networks.\" ICLR 2017.\n\n[3] Rombach et al. \"High-resolution image synthesis with latent diffusion models.\" CVPR 2022.\n\n[4] Xu et al. \"Stable target field for reduced variance score estimation in diffusion models.\" ICLR 2023.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "1. The paper is very well-written and easy to follow. I really enjoy the presentation flow and the thought process from Eq.7 to Eq.9 to Eq.10, with clear reasoning behind each change.\n2. The method is intuitive and simple, yet clever and effective. Utilization of importance sampling by time-dependent density ratio estimation (DRE) in diffusion models is novel and natural. DRE becomes more precise as $t$ becomes larger.\n3. I also appreciate the authors' efforts in providing toy examples and figures, which further makes the paper easy to understand.\n4. The problem the paper proposes to study is an important one, as real-world datasets are never short of biases, especially the unannotated ones.\n5. The proposed method's empirical performance is convincing. I also appreciate the inclusion of Eq.7 training numbers for the ablation study.", "weaknesses": "I do not have any major complaints. I list my minor questions and suggestions in the Questions section below.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "NWOQDnZXti", "reviewer": "Reviewer_WcK7", "summary": "This paper proposed a method to train an unbiased diffusion model with a weak supervision setting based on a sampling process that they called time-independent importance reweighting. They first analyzed why they should use the time-independent importance reweighting, then how to apply score matching to the reweighting process.", "questions": "N/A", "limitations": "", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The paper builds on successful recent advances in diffusion models, which excel in high-fidelity image generation within generative learning frameworks. Thus, the proposed TIW method shows promise for diverse applications, including text-to-image generation, image-to-image translation, and video generation.\n2. The paper addresses the understudied issue of dataset bias in generative modeling, introducing a method to enhance the fairness and reliability of ML systems.\n3.The paper establishes a theoretical equivalence between the proposed method and existing score-matching objectives from unbiased distributions, which could provide a strong foundation for the validity of their approach.", "weaknesses": "1. The paper builds upon a large body of previous work, which while showing the paper’s relevance, also means that any limitations or issues in those previous works could potentially affect the validity and effectiveness of TIW. The actually implementation process is similar to previous work on GAN.\n2. The paper shows that it mitigates the bias in the dataset, but I am not sure whether that method would influence the overall generation quality. It is important to see detailed qualitative and quantitative analysis.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "JopdKhC6R4", "reviewer": "Reviewer_irEP", "summary": "This paper addresses the issue of dataset bias in diffusion models. Authors introduces a novel method called Time-dependent Importance reWeighting (TIW). This method, leveraging a time-dependent density ratio, offers improvements in both reweighting and score correction processes. One of its major contributions is making the weighting objective more manageable and drawing a theoretical link to traditional score-matching objectives that aim for unbiased distributions. Experiments shows TIW outperforms other baselines.", "questions": "Can this method be transferred to other models like GAN-based model?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The problem this paper tries to address is important.\n\n2. The methodology introduced is innovative.\n\n3. This research creates a theoretical bridge between the proposed objective and the conventional score-matching objectives, offering a robust guarantee.\n\n4. Extensive testing of the method across diverse datasets and under varied conditions underscores its robustness and versatility.\n\n5. Preliminary results from the experiments are encouraging.", "weaknesses": "1. Introducing time-dependent methods might lead to heightened computational complexities in contrast to their time-independent counterparts. It would be beneficial to include a comparative analysis or discussion addressing this aspect.\n\n2. One pivotal query that emerges is whether the efficiency and overall success of the proposed method are intrinsically tied to the performance of the time-dependent discriminator. It would be enlightening to elucidate this relationship.\n\n3. There's a pertinent concern regarding the model's robustness. If the model isn't aptly regularized or subjected to limited training data, it might inadvertently heighten the risk of overfitting.\n\n4. The research paper titled \"Fair Diffusion\" by Friedrich et al. [1] is notably aligned with the theme of fairness in diffusion models. However, its conspicuous absence in the current work, either as a benchmark or a referenced study, is intriguing. The authors might want to consider explicating their rationale behind not incorporating it as a baseline or offering a comparative analysis. \n\n\n[1] Friedrich et al. \"Fair Diffusion: Instructing Text-to-Image Generation Models on Fairness.\"", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (poster)