Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces

Javier E. Santos, Zachary R. Fox, Nicholas Lubbers, Yen Ting Lin
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:9034-9059, 2023.

Abstract

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce “Blackout Diffusion”, which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-santos23a, title = {Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces}, author = {Santos, Javier E. and Fox, Zachary R. and Lubbers, Nicholas and Lin, Yen Ting}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {9034--9059}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/santos23a/santos23a.pdf}, url = {https://proceedings.mlr.press/v202/santos23a.html}, abstract = {Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce “Blackout Diffusion”, which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.} }
Endnote
%0 Conference Paper %T Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces %A Javier E. Santos %A Zachary R. Fox %A Nicholas Lubbers %A Yen Ting Lin %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-santos23a %I PMLR %P 9034--9059 %U https://proceedings.mlr.press/v202/santos23a.html %V 202 %X Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce “Blackout Diffusion”, which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.
APA
Santos, J.E., Fox, Z.R., Lubbers, N. & Lin, Y.T.. (2023). Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:9034-9059 Available from https://proceedings.mlr.press/v202/santos23a.html.

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