ReSWD: Steady Like ReSTIR - Variance Reduction by Combining Reservoir Sampling and Sliced Wasserstein Distance

Distribution matching is a core challenge in vision and graphics, but directly computing Wasserstein distance in high-dimensional distributions is too costly. Sliced Wasserstein Distance (SWD), which replaces it, is more scalable, but the high variance of the Monte Carlo estimator causes gradients to fluctuate and slows convergence.

To address this, we propose Reservoir SWD (ReSWD). This method integrates Weighted Reservoir Sampling into SWD, allowing informative projection directions to be better preserved during optimization. As a result, gradients become more stable while maintaining the unbiased property.

Experiments were conducted on synthetic benchmarks and real-world tasks including color correction and diffusion guidance.

• ReSWD consistently outperformed standard SWD.
• It also outperformed other existing variance reduction baselines.
• The key benefit lies in achieving faster and more stable optimization with less fluctuation.