Bridging Physically Based Rendering and Diffusion Models with Stochastic Differential Equation

TL;DR

This paper introduces a unified stochastic differential equation framework that connects physically based rendering and diffusion models, enabling physically grounded control over generated images and materials.

Contribution

It proposes a novel SDE formulation bridging Monte Carlo rendering and diffusion models, allowing physical control in generative image tasks.

Findings

Enables physically grounded control over diffusion-generated results

Successfully applies to rendering and material editing tasks

Provides a systematic analysis of physical characteristics in diffusion models

Abstract

Diffusion-based image generators excel at producing realistic content from text or image conditions, but they offer only limited explicit control over low-level, physically grounded shading and material properties. In contrast, physically based rendering (PBR) offers fine-grained physical control but lacks prompt-driven flexibility. Although these two paradigms originate from distinct communities, both share a common evolution -- from noisy observations to clean images. In this paper, we propose a unified stochastic formulation that bridges Monte Carlo rendering and diffusion-based generative modeling. First, a general stochastic differential equation (SDE) formulation for Monte Carlo integration under the Central Limit Theorem is modeled. Through instantiation via physically based path tracing, we convert it into a physically grounded SDE representation. Moreover, we provide a systematic analysis of how the physical characteristics of path tracing can be extended to existing diffusion models from the perspective of noise variance. Extensive experiments across multiple tasks show that our method can exert physically grounded control over diffusion-generated results, covering tasks such as rendering and material editing.