Neural Parametric Mixtures for Path Guiding

TL;DR

This work tackles the inefficiencies and artifacts of traditional path guiding by replacing spatial subdivision-based distributions with Neural Parametric Mixtures (NPM), a continuous implicit neural representation that encodes spatio-directional target distributions and decodes them into von Mises-Fisher mixtures for efficient sampling. NPM supports both incident radiance and full integrand (product) sampling, trained via gradient-based optimization on noisy Monte Carlo radiance estimates, enabling online learning and GPU-friendly parallelism. The approach yields improved capture of spatio-directional correlations, faster convergence with smaller training budgets, and competitive render-time performance across multiple scenes. While limited by a fixed number of mixture components, the method offers a practical framework with clear avenues for future work in adaptive mixtures, more efficient architectures, and extensions to bidirectional path tracing.

Abstract

Previous path guiding techniques typically rely on spatial subdivision structures to approximate directional target distributions, which may cause failure to capture spatio-directional correlations and introduce parallax issue. In this paper, we present Neural Parametric Mixtures (NPM), a neural formulation to encode target distributions for path guiding algorithms. We propose to use a continuous and compact neural implicit representation for encoding parametric models while decoding them via lightweight neural networks. We then derive a gradient-based optimization strategy to directly train the parameters of NPM with noisy Monte Carlo radiance estimates. Our approach efficiently models the target distribution (incident radiance or the product integrand) for path guiding, and outperforms previous guiding methods by capturing the spatio-directional correlations more accurately. Moreover, our approach is more training efficient and is practical for parallelization on modern GPUs.

Figures (8)

• Figure 1: Parallax issue caused by spatial discretizations (a). For a subdivided volume $\mathcal{S}(\mathbf{x})$ in (a), the guiding distribution is marginalized with training samples scattered over the volume $\mathcal{S}(\mathbf{x})$, and is shared by different positions (e.g., $\mathbf{x}_1$ and $\mathbf{x}_2$). Our method will not suffer from parallax due to NPM implicitly representing a monolithic function, continuously mapping from spatial positions to parametric guiding distributions, as shown in (b).
• Figure 2: High-level illustration of our Neural Parametric Mixtures (NPM). We implicitly encode the spatially varying target distributions with the multi-resolution embedding. When the distribution of a spatial location $\mathbf{x}$ is queried, (1) the features assigned to the nearby grid points surrounding $\mathbf{x}$ are interpolated at each level, and concatenated with other levels to obtain the spatial embedding $G(\mathbf{x})$. (2) the spatial embedding is then combined with other inputs to (3) feed into the lightweight MLP for (4) decoding the parameters $\Theta$ of the vMF mixture $\mathcal{V} (\omega_i \mid \Theta)$ with $K$ components. We then (5) use this parametric distribution for importance sampling the scattering direction. The result MC radiance estimate $\langle L_{\mathrm{i}}(\mathbf{x}, \omega_i) \rangle$ is used to estimate the training gradient $\nabla_\Theta D_{\mathrm{KL}}$ (Sec. \ref{['ssec:trainnpm']}), which is then back-propagated through these differentiable stages to optimize our NPM representation (dashed lines).
• Figure 3: Equal-sample-count ($\text{750spp}$) comparisons for two scenes. We show the error (for both the zoom-in areas and whole images) and time cost of different methods. The yellow plots (as well as the other figures) refer to the results obtained by unidirectional path tracing.
• Figure 4: Visual comparisons using the same experimental setup with Fig. \ref{['fig:core_comp']}, all are rendered with 750spp at $1280\times 720$. We use the online training setup for all the guiding methods, i.e., all the samples are included in the final rendering. Our method exhibits better performance than other guiding methods in most scenes by only learning the incident radiance term while further reducing the error by incorporating the BSDF term (i.e., product sampling). More results on other test scenes, additional error metrics and false-color visualizations are provided in our supplementary interactive viewer.
• Figure 5: Convergence plots correspond to Fig. \ref{['fig:core_comp']} and Fig. \ref{['fig:overall']}. Unidirectional path tracing with BSDF importance sampling (PT-BSDF), Practical Path Guiding muller2019path, Variance-aware Path Guiding rath2020variance and our method with different target distributions ($\text{NPM-{radiance}}$ and $\text{NPM-{product}}$). Our methods consistently outperform these classical guiding methods, and quickly become effective even with a few training samples and short training time (e.g., 30spp, amounting to about 3 seconds on GPU), indicating practicality for preview or even interactive rendering. We attribute this success to the compact implicit representation and better spatial resolution of our method. The image results and detailed statistics could be inspected in the supplemental materials.