RadioGS: Radiometrically Consistent Gaussian Surfels for Inverse Rendering

Conference: ICLR 2026 arXiv: 2603.01491 Code: https://qbhan.github.io/radiogs-page/ Area: 3D Vision Keywords: Inverse Rendering, Gaussian Splatting, Indirect Illumination, Radiometric Consistency, Ray Tracing

TL;DR

RadioGS introduces a radiometric consistency loss that minimizes the residual between the learned radiance of each Gaussian surfel and its physically rendered radiance, providing physics-based supervision for unobserved directions. This forms a self-correcting feedback loop that enables accurate indirect illumination and material decomposition, while supporting relighting in minutes.

Background & Motivation

Background: Inverse rendering based on Gaussian Splatting has advanced rapidly, efficiently recovering geometry, materials, and lighting from multi-view images. However, accurately decomposing global illumination effects—especially indirect illumination and inter-surface reflections—remains a core challenge.

Limitations of Prior Work: Existing methods handle indirect illumination in two main ways: (1) treating indirect radiance as a learnable residual (e.g., R3DG, GS-IR), where unconstrained optimization leads to ambiguous decomposition of lighting and materials; (2) querying indirect radiance from pre-trained NVS Gaussian primitives (e.g., IRGS, SVG-IR), where pre-training is supervised only for training viewpoints, making radiance queried from unobserved directions potentially incorrect.

Key Challenge: NVS training constrains the radiance of Gaussians only in camera-visible directions, whereas indirect illumination requires querying radiance from arbitrary directions (including inter-surface reflection directions). The lack of supervision for unobserved directions leads to inaccurate indirect radiance, causing lighting to be incorrectly baked into surface materials.

Goal: To provide a physics-based constraint that enables Gaussian surfels to obtain correct radiance values even in unobserved directions, thereby accurately modeling indirect illumination and inter-surface reflections.

Key Insight: Drawing inspiration from self-training radiance caches—iteratively minimizing the rendering equation residual to drive Gaussian primitive radiance toward physically correct solutions.

Core Idea: Radiometric consistency enforces that the learned radiance \(L_\mathbf{G}\) of each Gaussian surfel agrees with its physically rendered radiance \(L_\mathbf{G}^{PBR}\) derived from the rendering equation, forming a self-correcting loop: reconstruction supervision from camera viewpoints propagates to indirect illumination terms, while physical rendering in turn constrains radiance in unobserved directions.

Method

Overall Architecture

The pipeline consists of two stages. In the initialization stage, a simplified radiometric consistency loss with split-sum approximation is combined with an NVS reconstruction loss to pre-train Gaussian surfels and establish stable geometry. In the inverse rendering stage, the full Monte Carlo radiometric consistency loss is jointly optimized with material smoothness and lighting prior losses to refine geometry, materials, and lighting. For relighting, geometry and materials are fixed, and only surfel radiance is fine-tuned under the new lighting (~2 minutes), after which rendering proceeds directly using surfel radiance (<10ms/frame).

Key Designs

1. Radiometric Consistency Loss:

   • Function: Provides physics-based supervision for surfel radiance in unobserved directions.
   • Mechanism: For each surfel at position \(x\) and outgoing direction \(\omega_o\), the physically rendered radiance is computed as \(L_\mathbf{G}^{PBR}(x,\omega_o) = \int f_r \cdot (V \cdot L_{dir} + L_{ind}) \cdot (\omega_i \cdot n_x) d\omega_i\), where visibility \(V\) and indirect radiance \(L_{ind}\) are obtained via 2D Gaussian ray tracing. The residual \(\mathcal{R}_\mathbf{G} = L_\mathbf{G} - L_\mathbf{G}^{PBR}\) defines the loss \(\mathcal{L}_{rad} = \mathbb{E}_{j,\omega_o}[\|\mathcal{R}_\mathbf{G}\|_1]\). Minimizing this residual creates a bidirectional feedback: physical rendering guides radiance in unobserved directions, while camera-constrained radiance propagates through indirect illumination terms to other surfels.
   • Design Motivation: The self-correcting loop relies on the fact that reconstruction losses at camera viewpoints ensure accuracy for a subset of directions; this accurate radiance propagates via ray tracing as indirect illumination to other surfels, which in turn constrains their radiance values.

2. 2D Gaussian Ray Tracing and Monte Carlo Sampling:

   • Function: Efficiently and differentiably obtains inter-surfel visibility and indirect radiance.
   • Mechanism: A 2D Gaussian ray tracer casts rays as \(\text{Trace}(x, \omega_i; \mathbf{G}) = (L_{trace}, T_{trace})\), where accumulated radiance \(L_{trace}\) serves as indirect radiance \(L_{ind}\) and \(1-T_{trace}\) serves as visibility \(V\). Monte Carlo estimation randomly samples \(N_g = 4096\) surfels per step, each uniformly sampling \(N_s = 64\) incident rays over its normal-defined hemisphere (totaling \(2^{18}\) rays), while also sampling random outgoing directions (unobserved) and camera directions (constrained).
   • Design Motivation: The 2D Gaussian ray tracer shares ray-splat intersection computations with Gaussian surfels, enabling seamless and differentiable integration. Sampling camera directions ensures that constrained radiance signals propagate to ray-traced surfels.

3. Fine-Tuning-Based Efficient Relighting:

   • Function: Rapidly adapts surfel radiance to new lighting conditions.
   • Mechanism: Given new lighting, only a few rounds of fine-tuning via minimization of \(\mathcal{L}_{rad}\) are required (~2 minutes). After fine-tuning, rendering from arbitrary viewpoints using surfel radiance directly is possible (<10ms/frame), without runtime ray tracing or per-surfel storage of multi-directional incident radiance.
   • Design Motivation: Traditional methods require runtime indirect radiance queries during relighting (expensive), whereas radiometric consistency fine-tuning allows surfels to directly "memorize" the correct radiance under new lighting.

Loss & Training

Initialization stage: \(\mathcal{L}_{init} = \mathcal{L}_{recon} + \mathcal{L}_{recon}^{PBR} + \lambda_{rad}\mathcal{L}_{rad} + \lambda_{dist}\mathcal{L}_{dist} + \lambda_n\mathcal{L}_n + \lambda_{ns}\mathcal{L}_{ns} + \lambda_m\mathcal{L}_m\) (split-sum approximation of radiometric consistency). Inverse rendering stage: \(\mathcal{L}_{inv} = \mathcal{L}_{init} + \lambda_{as}\mathcal{L}_{as} + \lambda_{rs}\mathcal{L}_{rs} + \lambda_{light}\mathcal{L}_{light}\) (full Monte Carlo radiometric consistency + material smoothness + lighting prior). The radiometric consistency weight is \(\lambda_{rad} = 0.2\) (inverse rendering) and \(1.0\) (relighting fine-tuning). Total training time is approximately 60 minutes on an RTX 4090.

Key Experimental Results

Main Results

Method	NVS PSNR↑	Normal MAE↓	Albedo PSNR↑	Relight PSNR↑	Training Time
TensoIR (NeRF)	35.09	4.10	29.27	28.58	4h
GS-IR	35.33	4.95	29.94	24.37	-
IRGS	-	-	-	-	-
SVG-IR	-	-	-	-	-
RadioGS	Best	Best	Best	Best	1h

RadioGS outperforms existing GS-based and NeRF-based methods on nearly all metrics on the TensoIR dataset while maintaining computational efficiency.

Ablation Study

Configuration	Relight PSNR	Notes
Full RadioGS	Best	Full Monte Carlo radiometric consistency
w/o radiometric consistency loss	Significant drop	Inaccurate indirect illumination
Split-sum only (no MC)	Drop	Approximation insufficient for complex reflections
w/o initialization-stage consistency	Drop	Unstable geometric foundation
Fine-tuning relight vs. RT relight	Slightly lower but much faster	<10ms vs. ~100ms

Key Findings

• The radiometric consistency loss is the central source of RadioGS's advantage—removing it substantially degrades relighting quality, confirming the necessity of physics-based constraints for indirect illumination modeling.
• The inter-surface reflection of a red light bulb on a yellow LEGO surface (TensoIR dataset) demonstrates RadioGS's precise modeling of inter-surface reflections, which competing methods tend to bake into albedo.
• The fine-tuning relighting strategy achieves quality close to ray-tracing-based relighting with only 2 minutes of training, while rendering an order of magnitude faster.

Highlights & Insights

• The self-correcting feedback loop design is particularly insightful—NVS supervision and physical constraints are complementary rather than competing: NVS constrains observed directions while physical rendering constrains unobserved directions, with the two connected through indirect illumination to form a closed loop.
• The simplified radiometric consistency in the initialization stage represents an important engineering insight—applying Monte Carlo sampling directly on unstable geometry causes training oscillations, and the split-sum approximation provides a smooth transition.
• Fine-tuning-based relighting converts the cost of runtime ray tracing into an offline fine-tuning cost, making it well-suited for applications requiring multi-frame rendering.

Limitations & Future Work

• The method assumes dielectric materials; its effectiveness on strongly specular materials such as metals has not been validated.
• The \(2^{18}\) ray traces per step still incur computational overhead, with training taking approximately one hour.
• Monte Carlo sampling may produce inaccurate estimates in regions with low surfel density.
• Fine-tuning relighting may require more iterations when lighting changes drastically (e.g., from indoor to outdoor settings).

Related Work & Insights

• vs. IRGS (Gu et al., 2024): IRGS also uses Gaussian ray tracing to optimize indirect radiance, but training signals still come exclusively from observed viewpoint images. RadioGS provides additional supervision for unobserved directions through physics-based constraints.
• vs. SVG-IR (Sun et al., 2025): SVG-IR queries indirect radiance from NVS pre-trained Gaussian point clouds, but pre-trained Gaussians are unconstrained in unobserved directions. RadioGS's radiometric consistency addresses this fundamental issue.
• vs. Neural Radiance Cache (Müller et al., 2021): Radiance caching is used for global illumination in forward rendering; RadioGS extends this concept to Gaussian primitives in inverse rendering.

Rating

• Novelty: ⭐⭐⭐⭐⭐ The self-correcting feedback loop via radiometric consistency loss is novel and physically motivated.
• Experimental Thoroughness: ⭐⭐⭐⭐ Evaluated on both synthetic and real datasets with thorough ablations.
• Writing Quality: ⭐⭐⭐⭐⭐ Problem motivation, method derivation, and experimental analysis are all exceptionally clear.
• Value: ⭐⭐⭐⭐⭐ Significant advancement in accurate indirect illumination modeling for GS-based inverse rendering.

Related Papers

• [CVPR 2026] SGS-Intrinsic: Semantic-Invariant Gaussian Splatting for Sparse-View Indoor Inverse Rendering
• [ICCV 2025] GeoSplatting: Towards Geometry Guided Gaussian Splatting for Physically-based Inverse Rendering
• [ICLR 2026] 3DGEER: 3D Gaussian Rendering Made Exact and Efficient for Generic Cameras
• [ICLR 2026] Color3D: Controllable and Consistent 3D Colorization with Personalized Colorizer
• [ICLR 2026] One2Scene: Geometric Consistent Explorable 3D Scene Generation from a Single Image