Diffusion models have provable convergence guarantees similar to optimization algorithms—reverse diffusions contract divergence exponentially fast, and discrete samplers achieve measurable stationarity bounds that don't depend on data convexity.
This paper connects optimization theory to diffusion models by proving that reverse-time diffusion processes contract Fisher divergence at exponential rates under strong convexity conditions. The authors also establish first-order stationarity bounds for practical discrete samplers, showing how optimization guarantees translate to sampling quality without requiring global convexity.