Latent Diffusion Counterfactual Explanations

We thank the reviewer for the constructive review. We are glad that the reviewer finds our method “straightforward and novel” and acknowledges that it “showed good performance”. Below we address the remaining concerns.

Related work

We are grateful that you brought this work [1] to our attention. We have included it in the updated manuscript. We would briefly mention the similarities as well as differences to our work for sake of completeness. Similar to our work, they also generate images from a latent space of a generative model that remain close to the original image. However, their focus is on obtaining positives for contrastive learning that maintain the semantics (i.e., class). In contrast, our work aims to understand which input features affect the classification of a classifier, thereby we also allow for (and promote) semantic changes.

Impact of the angular threshold

The angular threshold controls how much the gradients of the classifier are allowed to deviate from the implicit classifier without being considered adversarial. In the case of large masking (i.e., small angular threshold) this would often remove such gradients and replace them with some overwrite value (in our experiments zeros). Thus, we would have little to no guidance from the classifier. Consequently, our method would only receive guidance from the distance gradients and thereby reconstruct the original image. On the other hand, in case of a large angular threshold, our guidance mechanism will bypass adversarial changes that will flip the decision of the classifier without a semantic change in the counterfactual image.

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[1] Li, Yinqi, et al. "Optimal Positive Generation via Latent Transformation for Contrastive Learning." NeurIPS 2022.

We thank the reviewer for the constructive review. We are glad that the reviewer finds our consensus guidance mechanism “interesting and novel”. Below we address the remaining concerns.

Does our method extend to tabular data?

We note that the focus of our paper lies in visual counterfactual explanations, similar to previous works, e.g., [1,2]. Thus, we hope that the reviewer understands that generating counterfactuals for tabular data would be out-of-scope for the present work but may be a valuable future direction.

Despite this, we still would like to outline how our approach could be used for tabular data in future works. First, one would need to train a diffusion model, such as TabDDPM [3], on some tabular dataset, such as adult or churn2. Second, we would need to adjust the backward diffusion process, i.e., adopt the consensus guidance mechanism, and can then generate counterfactuals for tabular data.

Speed-ups of our method

Our method indeed significantly speeds-up counterfactual generation compared to previous work (see the penultimate paragraph in Section 4.2). However, the counterfactual generation process cannot be considered fast overall, as mentioned in our limitations section. Thus, it is a meaningful direction to further speed it up. One possible direction could be to distill the classifier behavior into the diffusion model. This effectively avoids the computationally-intensive computation of gradients at every iteration step and could significantly expedite counterfactual generation.

Complementary to aforementioned, another benefit of our method is its seamless integration with diffusion models, ensuring that any advancement in speed in the recently very active research field of (text-conditional foundation) diffusion models, e.g., stable diffusion, would directly echo in speed-ups for our method. In a similar vein, our method benefits from improved generative capabilities of such diffusion models.

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[1] Goyal, Yash, et al. "Counterfactual visual explanations." ICML 2019.

[2] Augustin, Maximilian, et al. "Diffusion visual counterfactual explanations." NeurIPS 2022.

[3] Kotelnikov, Akim, et al. "Tabddpm: Modelling tabular data with diffusion models." ICML 2023.

We thank the reviewer for taking the time to review our paper and provide constructive criticisms. We are happy to see that the reviewer finds that our method is “very simple and easy to apply” and that the paper is “easy to follow” overall. Below we address remaining concerns or questions of the reviewer.

While appreciating the valuable feedback by the reviewer, we feel that some of the scores, such as the contribution score of 1, may not be entirely reflected by the written feedback. For the sake of the discussion of our paper, we kindly ask for further clarification from the reviewer. We believe this will greatly contribute to the discussion of our paper.

Request for more formal writing

We would appreciate it if the reviewer could point out parts of the submission that should be improved w.r.t. their formality.

Added explanation to Algorithm 1

As suggested by the reviewer, we added a brief explanation of Algorithm 1 in the main body.

Some unrealistic counterfactual examples (e.g., Fig. 4(f))

We agree that the generated counterfactual examples, e.g., Fig. 4(f), are not perfect. However, note that they are better than the ones from previous works, e.g., Fig. 3(h), where the problem of smoothing of high-frequency details is also prevalent. The deficiency in preserving high-frequency details in LDCE also stems from the application of the counterfactual generation within the lower-dimensional latent space. Here, the autoencoder’s decoder just fills in the high-frequency details. Thus, a better decoder, such as OpenAI’s recent consistency decoder [1], may do a better job filling in these fine details. Besides aforementioned, note that, as can be observed in Fig. 3(h), that changes in grass texture may also indicate a model bias, which may be desirable in the context of counterfactual generation.

Discussion on Celeb-A HQ results

The experiments on Celeb-A HQ demonstrate that our method, LDCE, is competitive to methods that are specifically tailored for this dataset, i.e., they use generative models pretrained on Celeb-A HQ. In fact, our method typically achieves the first or second rank on most metrics (Table 6) and is only inferior to ACE on Celeb-A HQ.

However, we find that LDCE is clearly superior to ACE on the more challenging ImageNet dataset (Table 2) at the same time. Arguably, “ImageNet is extremely complex and the classifier needs multiple factors for the decision-making process” [1, p.5] as argued by the authors of ACE. Note that this comparison is an apples-to-apples comparison of the methods, as LDCE-cls also uses a diffusion model that has been trained on ImageNet. It is worth noting that LDCE-txt, which uses stable diffusion as a diffusion model, is also superior to ACE.

Henceforth, we posit that the diminished performance observed on the domain-specific facial data from CelebA HQ can be attributed to the characteristics of the underlying diffusion model used in a specific counterfactual method. In fact, stable diffusion is renowned for its challenges in accurately generating faces and individuals [2]; a point openly acknowledged in both our limitations section and Appendix K. Nonetheless, the inherent merit of employing a non-domain-specific generative model - which has not been done before for counterfactual generation with generative models to the best of our knowledge - lies in its versatility, rendering it applicable across diverse datasets (as demonstrated on CelebA HQ). This flexibility becomes particularly valuable in real-world scenarios, where constraints on data accessibility are prevalent or pose significant challenges.

Though, if one has access to domain data, it is definitely beneficial to utilize it. To adapt our method, one could use low-rank adaptation that finetunes an existing stable diffusion model without the need of extensive computational resources. We expect that this will improve performance also on domain-specific data distributions, such as Celeb-A HQ.

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[1] https://github.com/openai/consistencydecoder

[2] Jeanneret, Guillaume, Loïc Simon, and Frédéric Jurie. "Adversarial Counterfactual Visual Explanations." CVPR 2023.

[3] https://huggingface.co/stabilityai/stable-diffusion-2