Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces

• URL: http://arxiv.org/abs/2305.11089v1
• Date: Thu, 18 May 2023 16:24:12 GMT
• Title: Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces
• Authors: Javier E Santos, Zachary R. Fox, Nicholas Lubbers, Yen Ting Lin
• Abstract summary: We develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process. As an example, we introduce Blackout Diffusion'', which learns to produce samples from an empty image instead of from noise.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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