Rényi Sampling: Nonlinear Wasserstein Corrections for Diffusion Models

We introduce Rényi sampling, nonlinear corrections for pretrained denoising diffusion probabilistic models that require no diffusion-network retraining or semantic class guidance. Our construction generalizes Langevin correction from the Wasserstein gradient flow of Kullback–Leibler divergence to that of Rényi divergence. The stochastic corrector combines a pretrained score with an estimated density ratio, with the Rényi order $\alpha$ controlling local correction strength. We establish a moving-target dissipation identity showing that Rényi sampling reduces distributional mismatch throughout denoising while preserving the intended noisy-data marginals. We show that $\alpha <1$ helps to rectify mode deficits, while $\alpha >1$ removes excess mode representations. Relative to Langevin correction, $\alpha =0.7$ recovers $11-15\%$ of the rare-mode deficit, and $\alpha =1.3$ removes $25-46\%$ of excess rare mass for imbalanced Gaussian mixtures experiments. Extending our method to a face generation model trained on a $5\%$ cat-$95\%$ human data mixture, correction increases the generated cat proportion from $3.8\%$ under ancestral sampling to $4.6\%$, while improving cat Fréchet Inception Distance from $47.13$ to $45.16$. These results demonstrate the potential of Rényi correction to improve both distributional fidelity and generation quality during sampling. Our code is available anonymously at https://github.com/Anonymous-PaperSubmission/RenyiSamplingDDPM.