Research map / Image generation / Autoregressive and latent generation
Functional Diffusion
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Proposes functional diffusion, a diffusion model whose samples are continuous functions, realized with a transformer denoiser over context point samples for SDF and deformation-field generation.
Problem
Standard diffusion models operate on finite-dimensional grids or latents, which is costly for high-resolution and irregular or non-standard domains; the paper targets generative modeling directly over infinite-dimensional function data.
Approach
Diffusion is formulated in function space: noise is a random function, noised states are functions f_t = alpha_t f0 + sigma_t g, and the denoiser maps a context set of point samples and their values (plus a query coordinate) to a denoised function. Sampling only denoises a small context set, with arbitrary queries evaluated at the end.
Key results
- On sparse-point SDF prediction, the proposed method reaches Chamfer 0.101 and F-score 0.707, versus 0.144 / 0.608 for 3DShape2VecSet and 0.166 / 0.531 for OccNet.
- On deformation field generation, MSE (x10^4) is 6.91 for the proposed method versus 13.32 for 3DShape2VecSet.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use functional diffusion instead of 3DS2VS | SDF prediction from sparse surface observations · SDF prediction from sparse surface observations | Chamfer: 0.144 -> 0.101 | Helped |
| Use functional diffusion instead of 3DS2VS | SDF prediction from sparse surface observations · SDF prediction from sparse surface observations | F-Score: 0.608 -> 0.707 | Helped |
| Use functional diffusion instead of 3DS2VS | SDF prediction from sparse surface observations · SDF prediction from sparse surface observations | Boundary: 0.016 -> 0.012 | Helped |
| Use functional diffusion instead of OccNet | SDF prediction from sparse surface observations · SDF prediction from sparse surface observations | Eikonal: 0.032 -> 0.024 | Helped |
| Use functional diffusion instead of 3DS2VS | Deformation field generation · Deformation field generation | MSE (×104): 13.32 -> 6.91 | Helped |
Surprising findings
- Multiple different noise initializations converge to nearly identical deformation fields given the same condition.
Limitations
- Training requires substantial computational resources; scaling to large datasets such as Objaverse-XL would need more GPUs.
- Introduces an extra hyperparameter, the sampling rate of the sampled function representation, which must be explored during training.
Experimental setup
Datasets: signed distance functions of 3D shapes dynamic mesh sequences with sparse correspondence
Benchmarks: SDF prediction from 64-point sparse surface point clouds deformation field generation from 32 sparse correspondences
Metrics: Chamfer distance F-score Eikonal error boundary error MSE
Baselines: OccNet 3DShape2VecSet DPF
Builds on: DDPM DDIM DPF 3DShape2VecSet VDM
Closest papers by meaning
- Denoising Functional Maps: Diffusion Models for Shape Correspondence (CVPR 2025 · similarity 0.87)
- Fixed Point Diffusion Models (CVPR 2024 · similarity 0.86)
- Single Mesh Diffusion Models with Field Latents for Texture Generation (CVPR 2024 · similarity 0.86)
- On the Trajectory Regularity of ODE-based Diffusion Sampling (ICML 2024 · similarity 0.86)
- Diffuse Everything: Multimodal Diffusion Models on Arbitrary State Spaces (ICML 2025 · similarity 0.86)
- FAM Diffusion: Frequency and Attention Modulation for High-Resolution Image Generation with Stable Diffusion (CVPR 2025 · similarity 0.85)
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