ReSWD: ReSTIR‘d, not shaken. Combining Reservoir Sampling and Sliced Wasserstein Distance for Variance Reduction.

Distribution matching is central to many vision and graphicstasks, where the widely used Wasserstein distance is too costly to com-pute for high-dimensional distributions. The Sliced Wasserstein Distance(SWD) offers a scalable alternative, yet its Monte Carlo estimator suffersfrom high variance, resulting in noisy gradients and slow convergence. Weintroduce Reservoir SWD (ReSWD), which integrates Weighted Reser-voir Sampling into SWD to adaptively retain informative projectiondirections in optimization steps, resulting in stable gradients while re-maining unbiased. Experiments on synthetic benchmarks and real-worldtasks such as color correction and diffusion guidance show that ReSWDconsistently outperforms standard SWD and other variance reductionbaselines. Project page with code: https://ReservoirSWD.github.io