Title: ReSWD: ReSTIR‘d, not shaken. Combining Reservoir Sampling and Sliced Wasserstein Distance for Variance Reduction.
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: Sliced Wasserstein Distance, Variance Reduction, Weighted Reservoir Sampling, Color matching, Distribution matching, Optimal Transport

Abstract: Distribution matching is central to many vision and graphics tasks, where the widely used Wasserstein distance is too costly to compute for high dimensional distributions. The Sliced Wasserstein Distance (SWD) offers a scalable alternative, yet its Monte Carlo estimator suffers from high variance, resulting in noisy gradients and slow convergence. We introduce Reservoir SWD (ReSWD), which integrates Weighted Reservoir Sampling into SWD to adaptively retain informative projection directions in optimization steps, resulting in stable gradients while remaining unbiased. Experiments on synthetic benchmarks and real-world tasks such as color correction and diffusion guidance show that ReSWD consistently outperforms standard SWD and other variance reduction baselines.

TL;DR: Combining Reservoir Sampling and Sliced Wasserstein Distance for Variance Reduction for various matching applications.