Neural BRDF Importance Sampling by Reparameterization

TL;DR

This work introduces a reparameterization-based framework for neural BRDF importance sampling that reframes BRDF sampling as learning a change-of-variables transformation of the BRDF integral. By training a reparameterization T and an auxiliary pdf estimator, the method achieves unbiased MIS integration without requiring invertible networks, enabling single-step sampling with flexible networks and significant variance reduction. Empirical results show strong variance-speed advantages, particularly for specular materials, with efficient CUDA-backed inference and competitive or superior performance to flow-based and diffusion baselines. The approach broadens the applicability of neural BRDFs in physically-based rendering by delivering both accuracy and efficiency in Monte Carlo rendering pipelines.

Abstract

Neural bidirectional reflectance distribution functions (BRDFs) have emerged as popular material representations for enhancing realism in physically-based rendering. Yet their importance sampling remains a significant challenge. In this paper, we introduce a reparameterization-based formulation of neural BRDF importance sampling that seamlessly integrates into the standard rendering pipeline with precise generation of BRDF samples. The reparameterization-based formulation transfers the distribution learning task to a problem of identifying BRDF integral substitutions. In contrast to previous methods that rely on invertible networks and multi-step inference to reconstruct BRDF distributions, our model removes these constraints, which offers greater flexibility and efficiency. Our variance and performance analysis demonstrates that our reparameterization method achieves the best variance reduction in neural BRDF renderings while maintaining high inference speeds compared to existing baselines.

Figures (19)

• Figure 1: Toy example in 1D. Our model requires only a small MLP (2 hidden layers, 16 features) to learn the reparameterization of the target distribution to the prior distribution (plot 3 on top), inducing a more accurate importance sampling (plot 1 at bottom) than the baselines (plot 2-3 at bottom) when using a similar network. The bottom plots are generated by binning samples into 1D histograms.
• Figure 2: Choice of the prior distribution affects the sampling bias. Images are generated by binning samples to 2D histograms with red regions denoting zero samples. When using a distribution with compact support as the prior (left), samples generated by our model may not cover the low probability region of the target distribution (right), resulting in bias. The problem can be solved by using a Gaussian-like distribution that has infinite support (middle).
• Figure 3: Comparison between $\mathcal{L}_\text{rep}$ and $\mathcal{L}_\text{rep}'$. Optimizing $\mathcal{L}_\text{rep}$ (column 3) in most cases enables correct reconstructions of BRDF distributions and unbiased renderings (row 1-2). But it fails on mirror-like materials (row 3-4). This can be fixed by optimizing the upper bound $\mathcal{L}'_\text{rep}$ (column 4). The insets show the zoom-ins of reconstructed pdfs (row 1, 3) and the corresponding renderings (row 2, 4).
• Figure 4: MIS integrated into our model. The first row shows our pdf approximation $\hat{p}$ for MIS matches our sampling distribution (induced by $\mathbf{T}$) in the first image with little difference (4th image with number showing KL-divergence). The second row shows the rendering using emitter sampling (1st image), our BRDF sampling (2nd image), and the combination through MIS (3rd image), which is unbiased so matches the reference (4th image).
• Figure 5: Architectures of reparameterization network (left) and pdf approximation network (right).