Research map / Image generation / Fast diffusion sampling
Unified Framework for Diffusion Generative Models in SO(3): Applications in Computer Vision and Astrophysics
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Extends score-based and DDPM diffusion generative models to SO(3) using the tractable isotropic Gaussian heat kernel, and applies them to synthetic densities, symmetric-object pose estimation, and galaxy orientation modeling.
Problem
Standard diffusion models assume Euclidean geometry and do not transfer directly to manifold-valued data such as 3D rotations on SO(3), which arise in robotics, biochemistry and astrophysics.
Approach
Exploits the closed-form heat kernel of SO(3) (isotropic Gaussian, closed under convolution) so forward noising can be sampled directly without simulating SDEs; trains a score network with denoising score matching and samples via a geometric Heun ODE solver (RK-MK), with a DDPM variant using an isotropic Gaussian reverse kernel and ELBO-based loss.
Key results
- SO(3) SGM achieves the best C2ST on all three synthetic densities (0.50 on checkerboard, 4-Gaussians, 0.51 on 3-Stripes), beating RSGM, Moser Flow, DDPM and Implicit-PDF.
- The SO(3) DDPM gets 0.52-0.53 C2ST, far better than the baseline DDPM (0.71 to 0.90) on the same densities.
- On IllustrisTNG galaxy orientations, the SGM reproduces the omega(r) correlation of major and minor axes well, and captures the weak intermediate-axis signal with statistical consistency.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SGM on SO(3) instead of RSGM | SO(3) generative modeling · SO(3) Checkerboard | C2ST: 0.51 ± 0.01 -> 0.50 ± 0.01 | Helped |
| Use SGM on SO(3) instead of Moser Flow | SO(3) generative modeling · SO(3) 4-Gaussians | C2ST: 0.60 ± 0.02 -> 0.50 ± 0.01 | Helped |
| Use SGM on SO(3) instead of RSGM | SO(3) generative modeling · SO(3) 3-Stripes | C2ST: 0.51 ± 0.01 -> 0.51 ± 0.01 | No clear effect |
| Use SGM on SO(3) instead of DDPM on SO(3) | SO(3) generative modeling · SO(3) Checkerboard | C2ST: 0.52 ± 0.01 -> 0.50 ± 0.01 | Helped |
| Use SGM on SO(3) instead of DDPM on SO(3) | SO(3) generative modeling · SO(3) 4-Gaussians | C2ST: 0.53 ± 0.01 -> 0.50 ± 0.01 | Helped |
| Use SGM on SO(3) instead of DDPM on SO(3) | SO(3) generative modeling · SO(3) 3-Stripes | C2ST: 0.52 ± 0.01 -> 0.51 ± 0.01 | Helped |
| Use rotation-matrix inputs instead of axis-angle inputs (ablation) | SO(3) neural diffusion models · Partially trained sampled distributions | distribution continuity | Helped |
| Use a continuous 6D output rotation representation instead of axis-angle outputs (ablation) | SO(3) DDPM · Fully trained sampled distributions | distribution quality | No clear effect |
| Use 3x3 rotation-matrix inputs instead of axis-angle inputs (ablation) | SO(3) neural diffusion models · Fully trained sampled distributions | distribution quality | No clear effect |
Surprising findings
- The RSGM baseline is reported to be about 8x slower per training batch than the proposed SGM because of simulating the forward SDE during training.
- The DDPM loss of prior work does not transfer directly to SO(3), causing a failure mode in that baseline's density estimates.
Limitations
- DDPM variant has larger-variance training loss and produces less sharp distributions than the SGM.
- Intermediate-axis galaxy alignment signal is very weak and small-scale correlations deviate from simulation.
- Only SO(3) is addressed; the method relies on SO(3)-specific heat kernel and does not generalize to arbitrary manifolds.
Experimental setup
Datasets: synthetic SO(3) densities (checkerboard, 4-Gaussians, 3-Stripes) SYMSOL IllustrisTNG TNG100-1 simulation
Benchmarks: synthetic SO(3) densities (checkerboard, 4-Gaussians, 3-Stripes) SYMSOL pose estimation IllustrisTNG galaxy orientation correlation
Metrics: C2ST correlation function omega(r) qualitative density plots
Baselines: RSGM Moser Flow DDPM on SO(3) (Sheng et al.-style) Implicit-PDF
Builds on: score-based generative models (Song et al.) DDPM Riemannian score-based generative models Implicit-PDF Moser flow
Closest papers by meaning
- Generative Modeling on Manifolds Through Mixture of Riemannian Diffusion Processes (ICML 2024 · similarity 0.88)
- Dynamic Diffusion Schrödinger Bridge in Astrophysical Observational Inversions (NeurIPS 2025 · similarity 0.87)
- Improving the Euclidean Diffusion Generation of Manifold Data by Mitigating Score Function Singularity (NeurIPS 2025 · similarity 0.87)
- Adaptive 3D Reconstruction via Diffusion Priors and Forward Curvature-Matching Likelihood Updates (NeurIPS 2025 · similarity 0.87)
- Diffusion Model's Generalization Can Be Characterized by Inductive Biases toward a Data-Dependent Ridge Manifold (NeurIPS 2026 · similarity 0.87)
- Harmonizing Geometry and Uncertainty: Diffusion with Hyperspheres (ICML 2025 · similarity 0.87)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.