Sample Space Partitioning and Spatiotemporal Resampling for Specular Manifold Sampling

Caustics rendering remains a long-standing challenge in Monte Carlo rendering because high-energy specular paths occupy only a small region of path space, making them difficult to sample effectively. Recent work such as Specular Manifold Sampling (SMS) [Zeltner et al. 2020] can stochastically sample these specular paths and estimate their unbiased weights using Bernoulli trials. However, applying SMS in interactive rendering is non-trivial because it is slow and delivers noisy images given a very limited time budget.

In this work, we extend SMS for high-quality caustic rendering in interactive settings using sample space partitioning. Our insight is that Newton iterations, the main performance bottleneck of SMS, can be restricted to the vicinity of the seed path, which can dramatically improve the performance. We achieve this with tile-based sample space partitioning, which bounds the manifold walk region and allows building a per-frame prior distribution that concentrates initial guesses around solutions. This reduces the cost of SMS and improves its sampling quality. Applying spatiotemporal reuse (ReSTIR) further amortizes the sample generation cost, greatly increasing the effective sample count. As a result, we achieve significant variance reduction compared to SMS in interactive rendering scenarios.

Source Code

An implementation of our Sample Space Partitioning method with ReSTIR is implemented in Falcor 8.0 as a rendering module named PSMSReSTIR (Partitioned-SMS ReSTIR).

Comparisons

Comparison Selection:

Path Tracing
(18 ms)

SMS
(21 ms)

Ours with ReSTIR
(18 ms)

Reference

Path Tracing
(35 ms)

SMS
(118 ms)

Ours with ReSTIR
(35 ms)

Reference

Path Tracing
(24 ms)

SMS
(40 ms)

Ours with ReSTIR
(24 ms)

Reference

Path Tracing
(85 ms)

SMS
(117 ms)

Ours with ReSTIR
(77 ms)

Reference

Interactive Results Viewer

We provide an interactive comparison of the full images in Figure 1 and 4. Click an scene thumbnail or link to see results for the scene/figure.

(We recommend using Chrome or Microsoft Edge for the best experience.)

PlaneAndSlab (Figure 1)

Slab (Figure 4)

Plane (Figure 4)

Pool (Figure 4)

Fast Forward Video

Paper Video

Project Publications

Pengpei Hong, Meng Duan, Beibei Wang, Cem Yuksel, Tizian Zeltner, Daqi LinSample Space Partitioning and Spatiotemporal Resampling for Specular Manifold SamplingSIGGRAPH Asia 2025 Conference Papers

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