Why Gaussian Diffusion Models Fail on Discrete Data?
This addresses a key bottleneck for applying diffusion models to discrete data, which is incremental but important for domains like text and protein generation.
The paper investigated why Gaussian diffusion models struggle with discrete data, identifying a critical sampling interval where data density becomes multimodal, causing the DDPM solver to produce out-of-distribution inputs and degrade sample quality. They showed that combining self-conditioning with a q-sampling solver within this interval improves generation quality, validated across text, code, and protein domains.
Diffusion models have become a standard approach for generative modeling in continuous domains, yet their application to discrete data remains challenging. We investigate why Gaussian diffusion models with the DDPM solver struggle to sample from discrete distributions that are represented as a mixture of delta-distributions in the continuous space. Using a toy Random Hierarchy Model, we identify a critical sampling interval in which the density of noisified data becomes multimodal. In this regime, DDPM occasionally enters low-density regions between modes producing out-of-distribution inputs for the model and degrading sample quality. We show that existing heuristics, including self-conditioning and a solver we term q-sampling, help alleviate this issue. Furthermore, we demonstrate that combining self-conditioning with switching from DDPM to q-sampling within the critical interval improves generation quality on real data. We validate these findings across conditional and unconditional tasks in multiple domains, including text, programming code, and proteins.