ReSWD: ReSTIR'd, not shaken. Combining Reservoir Sampling and Sliced
  Wasserstein Distance for Variance Reduction
Authors: name: Mark Boss, name: Andreas Engelhardt, name: Simon Donné, name: Varun Jampani
Organization: Stability AI

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. Project page: https://reservoirswd.github.io/