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This paper investigates the failure of Gaussian diffusion models with DDPM solvers when applied to discrete data represented as a mixture of delta-distributions. They identify a critical sampling interval where the noisified data becomes multimodal, causing DDPM to sample from low-density regions and generate out-of-distribution samples. The authors demonstrate that self-conditioning and a novel q-sampling solver can mitigate this issue, and combining both techniques improves generation quality across text, code, and protein data.
Gaussian diffusion models stumble on discrete data because of a multimodality problem during denoising, but a clever combo of self-conditioning and a new "q-sampling" solver can get them back on track.
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.