Skipping the Zeros in Diffusion Models for Sparse Data Generation
For practitioners working with sparse continuous data (e.g., in physics and biology), this work offers a method to improve efficiency and quality over standard diffusion models.
Diffusion models struggle with sparse continuous data because they do not model exact zeros, erasing sparsity patterns and wasting computation. The proposed Sparsity-Exploiting Diffusion (SED) models only non-zero values, preserving sparsity and reducing computation while matching or improving generation quality on physics and biology benchmarks.
Diffusion models (DMs) excel on dense continuous data, but are not designed for sparse continuous data. They do not model exact zeros that represent the deliberate absence of a signal. As a result, they erase sparsity patterns and perform unnecessary computation on mostly zero entries. With Sparsity-Exploiting Diffusion (SED), we model only non-zero values, preserving sparsity. SED delivers computational savings while maintaining or improving generation quality by skipping zeros during training and inference. Across physics and biology benchmarks, SED matches or surpasses conventional DMs and domain-specific baselines, while vision experiments provide intuitive insights into the limitations of dense DMs and the benefits of SED.