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TensoFlow: Tensorial Flow-based Sampler for Inverse Rendering
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Proposes TensoFlow, a learnable spatially and directionally aware importance sampler for inverse rendering, parameterized by tensorial normalizing flows with piecewise-quadratic coupling layers.
Problem
Inverse rendering needs Monte Carlo evaluation of the rendering equation, but pre-defined importance samplers (cosine-weighted, GGX) fail to match the spatially and directionally varying integrand, causing high variance.
Approach
Learn the importance sampler itself as a normalizing flow (piecewise-quadratic coupling layers) conditioned on a tensorial spatial feature and the reflected direction, trained by cross-entropy between the integrand and the flow's PDF, giving both sampling and PDF inference.
Key results
- On the TensoSDF synthetic dataset, TensoFlow averages 26.933 PSNR, 0.938 SSIM, and 0.0659 LPIPS, versus 25.971 PSNR for TensoSDF.
- On Stanford-ORB, average PSNR improves from 29.683 (TensoSDF) to 29.957 with TensoFlow.
- Ablation: replacing the learned flow with a single shared sampler drops PSNR from 26.933 to 25.196.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use learnable diffuse and specular samplers | TensoFlow · TensoSDF synthetic (Average) | PSNR: 25.971 -> 26.933 | Helped |
| use TensoFlow rather than TensoSDF | TensoFlow · Stanford-ORB (Average) | PSNR: 29.683 -> 29.957 | Helped |
| add a learnable diffuse sampler rather than use a pre-defined diffuse sampler (ablation) | TensoFlow · TensoSDF synthetic (Average) | PSNR: 26.433 -> 26.933 | Helped |
| add a learnable specular sampler rather than use a pre-defined specular sampler (ablation) | TensoFlow · TensoSDF synthetic (Average) | PSNR: 26.203 -> 26.933 | Helped |
| use separate flow samplers for diffuse and specular terms (ablation) | TensoFlow · TensoSDF synthetic (Average) | PSNR: 25.196 -> 26.933 | Helped |
| model the half vector rather than the incident direction (ablation) | TensoFlow · TensoSDF synthetic (Average) | PSNR: 26.474 -> 26.933 | Helped |
| add the tensorial spatial feature to the flow (ablation) | TensoFlow · TensoSDF synthetic (Average) | PSNR: 26.058 -> 26.933 | Helped |
| add the reflected direction input to the flow (ablation) | TensoFlow · TensoSDF synthetic (Average) | PSNR: 25.876 -> 26.933 | Helped |
| increase specular samples from 32 to 128 rays (ablation) | TensoFlow · TensoSDF synthetic (Average) | PSNR: 25.849 -> 26.933 | Helped |
| increase specular samples from 64 to 128 rays (ablation) | TensoFlow · TensoSDF synthetic (Average) | PSNR: 26.440 -> 26.933 | Helped |
Surprising findings
- Modeling the half vector distribution works better than modeling the incident direction directly (26.474 vs 26.933 PSNR without it).
Limitations
- Normalizing flow sampling is slower because each sampled direction requires a flow query.
- Gains on Stanford-ORB are smaller than on the synthetic dataset, attributed to simpler geometry and lighting.
Experimental setup
Datasets: TensoSDF synthetic dataset Stanford-ORB
Benchmarks: TensoSDF synthetic dataset Stanford-ORB
Metrics: PSNR SSIM LPIPS
Baselines: TensoIR NeRO NeILF++ TensoSDF
Builds on: TensoSDF NICE piecewise-quadratic coupling flows NeRO TensoRF
Closest papers by meaning
- Inverse Rendering using Multi-Bounce Path Tracing and Reservoir Sampling (ICLR 2025 · similarity 0.84)
- Uni-Renderer: Unifying Rendering and Inverse Rendering Via Dual Stream Diffusion (CVPR 2025 · similarity 0.82)
- Fast samplers for Inverse Problems in Iterative Refinement models (NeurIPS 2024 · similarity 0.82)
- Solving Inverse Problems with FLAIR (NeurIPS 2025 · similarity 0.81)
- VMINer: Versatile Multi-view Inverse Rendering with Near- and Far-field Light Sources (CVPR 2024 · similarity 0.81)
- Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving (NeurIPS 2025 · similarity 0.81)
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