Unified Discrete Diffusion for Categorical Data

• URL: http://arxiv.org/abs/2402.03701v2
• Date: Mon, 12 Aug 2024 16:22:38 GMT
• Title: Unified Discrete Diffusion for Categorical Data
• Authors: Lingxiao Zhao, Xueying Ding, Lijun Yu, Leman Akoglu,
• Abstract summary: We present a series of mathematical simplifications of the variational lower bound that enable more accurate and easy-to-optimize training for discrete diffusion. We derive a simple formulation for backward denoising that enables exact and accelerated sampling, and importantly, an elegant unification of discrete-time and continuous-time discrete diffusion.
• Score: 37.56355078250024
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Discrete diffusion models have seen a surge of attention with applications on naturally discrete data such as language and graphs. Although discrete-time discrete diffusion has been established for a while, only recently Campbell et al. (2022) introduced the first framework for continuous-time discrete diffusion. However, their training and sampling processes differ significantly from the discrete-time version, necessitating nontrivial approximations for tractability. In this paper, we first present a series of mathematical simplifications of the variational lower bound that enable more accurate and easy-to-optimize training for discrete diffusion. In addition, we derive a simple formulation for backward denoising that enables exact and accelerated sampling, and importantly, an elegant unification of discrete-time and continuous-time discrete diffusion. Thanks to simpler analytical formulations, both forward and now also backward probabilities can flexibly accommodate any noise distribution, including different noise distributions for multi-element objects. Experiments show that our proposed USD3 (for Unified Simplified Discrete Denoising Diffusion) outperform all SOTA baselines on established datasets. We open-source our unified code at https://github.com/LingxiaoShawn/USD3.

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