Degenerate diffusion models—where the noise schedule breaks down—can still be guided effectively using causal optimal transport, enabling diffusion-based generation in settings where standard score-based methods fail.
This paper addresses a fundamental problem in diffusion models: how to guide generation when the model has a singular diffusion coefficient (degenerate case) and the underlying data distributions are irregular or non-smooth. The authors use causal optimal transport theory to define loss functions that enable effective guidance with minimal assumptions about the data.