Training Unbiased Diffusion Models From Biased Dataset

We appreciate the reviewer's sincere and helpful feedback. We answer for reviewer’s comments below.

Q1. [Computation Cost] 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.

Response to Q1.

Thank you for addressing important issues. We compare the computation cost of time-independent importance reweighting (IW-DSM), and time-dependent importance reweighting (TIW-DSM) in terms of 1) training time, 2) training memory, 3) sampling time, and 4) sampling memory.

Both methods require the evaluation of the discriminator for diffusion model training. However, TIW demands 34% more training time and 13% more training memory compared to IW-DSM. This is because we need to compute a new term $\nabla \log{w^t_{\phi}}(x_t)$ using the automatic gradient module in the PyTorch, while IW-DSM only requires a feed-forward value. However, once the training is complete, the discriminator is not used for sampling, so the sampling time & memory remain the same. We conducted tests on RTX 4090 * 4 Cores on CIFAR-10 experiments. We also reflect it in Appendix D.5. Note that the training of time-dependent discriminator is negligibly cheap, converging around 10 minutes with 1 RTX 4090.

Thank you for your detailed rebuttals. After reading all the rebuttals, including those from other reviewers, I would like to adjust my initial score from 'borderline accept' (6) to 'weak accept' (7). Unfortunately, there isn't a specific selection for 'weak accept,' as the next available option is 'accept' with a score of 8. Therefore, I have decided to increase my confidence in my assessment to 4.

To all ACs and SACs, please consider my suggestions as a 'weak accept.' Thank you for your understanding.

We appreciate the reviewer's feedback. We answer for reviewer's comments below.

[Clarification on miscommunicated point]

In response to the reviewer's summary, we would like to kindly point out that there are some miscommunicated points. The proposed method, TIW-DSM in eq. (10) is based on time-dependent importance reweighting, which is distinctly different from IW-DSM which leverages time-independent importance reweighting in eq. (7). The reviewer seems to think of our method as IW-DSM, but IW-DSM is the baseline method. We will consider distinguishing the two methods with more easily understandable names for the final draft.

Q2. [Objective function interpolation] In theory, the method works if $E_{x_{0}\sim p_{bias}(x_{0}|x_{t})} [\nabla \log p(x_{t}|x_{0})] = \nabla \log p_{bias}^{t}(x_t)$ and DRE's gradient actually contains $\nabla \log p_{data}^{t}(x_t)$ 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.

[3] Rombach et al. "High-resolution image synthesis with latent diffusion models." CVPR 2022.

[4] Xu et al. "Stable target field for reduced variance score estimation in diffusion models." ICLR 2023.

Response to Q2.

We appreciate your sincere suggestions. We acknowledge your suggestion makes sense and have conducted experiments in Appendix E.7. We attempted hard truncation of two objectives at a specific time $\tau$ as described in eq. (54), which utilize $(0,\tau)$ for $L_{DSM}$ objective, and $(\tau, T)$ for $L_{TIW-DSM}$ objective. Contrary to the intuition, the performance in Figure 27 is just interpolated. One possible reason is the negative effects of hard truncation on the objectives. Giving a sharp difference at the boundary of $\tau$ might not have been favorable for the generation path. As you suggested, we are considering experiments involving the gradual interpolation of the two objectives and will include the results in the final draft.

We appreciate the reviewer for a deep understanding of our work and highly constructive suggestions. We answer the reviewer’s comments below.

Q1. [Time-dependent density ratio in GANs] 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.

[1] Wang et al. "Diffusion-gan: Training gans with diffusion." ICLR 2023.

[2] Arjovsky et al. "Towards principled methods for training generative adversarial networks." ICLR 2017.

Response to Q1.

We appreciate your valuable advice. We acknowledge the existence of several works that employ noise injection tricks in the discriminator input of GANs. We have thoroughly examined the papers you provided guidance on, along with additional relevant papers, and have summarized our findings in Appendix B.4.

Q3. [Overfitting on CIFAR-10 experiments] In Fig.4, every method's performance peaks early and gets worse. This is unexpected for me. Could the authors provide an explanation?

Response to Q3.

As we described in Appendix C, some literature reports that overfitting is correlated with training configurations in network architecture, EMA, and diffusion noise scheduling. One of our own observations is that overfitting becomes more pronounced as the number of data decreases, as shown in Figure 10.

Figure 4-(e) indicates that TIW-DSM shows less overfitting compared to IW-DSM. IW-DSM can not utilize the information from $D_{bias}$ effectively because time-independent density ratio provides extremely small reweighting value as shown in Figure 8-(a). On the other hand, TIW-DSM utilizes the information from $D_{bias}$ more effectively as shown in Figure 8-(b-d).

I want to thank the authors for addressing my questions, especially in Appendix E.7. The results are indeed surprising to me, and perhaps they suggest that the quality of DRE is actually good when heavily sharing parameters despite the difficulty of the task, or the existing understanding of the score field is incomplete.

I have read other reviewers' comments and the corresponding rebuttal, and I thank the authors for providing detailed responses. I still lean towards acceptance and thus keep my rating.

We appreciate the reviewer for the constructive and thoughtful feedback. We answer for reviewer’s comments below.

Q1. [Connection to text-to-image model] 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.

Response to Q1.

[Mitigate bias in text-to-image models] Thank you for your feedback. From the perspective of providing a text-to-image foundation model for practical use, addressing bias becomes a more crucial consideration. For instance, providing “nurse” as a condition results in the generation of only female nurses as shown in [a1] and Figure 28 in our paper. The proposed method introduces an approach to mitigate latent bias, so the proposed method could be applicable in this case. We constructed a reference dataset and fine-tuned the Stable Diffusion on the “nurse” prompt to mitigate bias on gender. The fine-tuned Stable Diffusion with the TIW-DSM objective successfully generates a certain proportion of male nurses as shown in Figure 29 (Please refer to Appendix E.8 for detailed explanations). This experiment demonstrates that our method works well in text-to-image diffusion models. In addition to fine-tuning, this approach can be applied to training a text-to-image model from scratch. Constructing a reference set for (prompt, bias) pairs deemed important by society and applying our objective during training, should enable a relatively fair generation.

[Dataset setting] Indeed, text-to-image models are trained based on explicit supervision of (text, image) pairs. On the other hand, the weak supervision setting we employ is cost-effective in terms of dataset collection. While we acknowledge the role of general-purpose models like Stable Diffusion, it is also crucial to develop task-specific models starting from the dataset collection phase. It’s worth noting that dataset collection with weak supervision is prevalent in companies [a2].

[a1] Maggio et al. The Bias problem: Stable Diffusion from https://vittoriomaggio.medium.com/the-bias-problem-stable-diffusion-607aebe63a37

[a2] 23 & me. The Real Issue: Diversity in Genetics Research retrieved from https://blog.23andme.com/articles/the-real-issue-diversity-in-genetics-research.