ReSWD: ReSTIR'd, not shaken. Combining Reservoir Sampling and Sliced Wasserstein Distance for Variance Reduction
This work addresses a bottleneck in distribution matching for vision and graphics tasks, offering a variance reduction method that improves optimization efficiency, though it is incremental as it builds on existing SWD techniques.
The paper tackled the high variance problem in Sliced Wasserstein Distance (SWD) estimators, which cause noisy gradients and slow convergence in distribution matching tasks, by introducing ReSWD, which integrates Weighted Reservoir Sampling to adaptively retain informative projection directions, resulting in stable gradients and outperforming standard SWD and other baselines in experiments on synthetic benchmarks and real-world tasks like color correction and diffusion guidance.
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/