Research map / Image generation / Fast diffusion sampling
A Score-Based Deterministic Diffusion Algorithm with Smooth Scores for General Distributions
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.
Proposes a deterministic (interacting-particle, porous-media-regularized) forward diffusion for score-based generative modeling so that scores stay bounded for compactly supported data, and shows it beats a stochastic forward process on toy data, binary MNIST and modified CIFAR-10.
Problem
Score-based diffusion models require the data log-gradient to be Lipschitz, which excludes compactly supported distributions, and stochastic forward processes yield exploding scores there.
Approach
Replace the Brownian forward SDE with a deterministic McKean-Vlasov process whose drift is the gradient of a mollified self-interaction kernel convolved with the current density; the resulting vector field is always Lipschitz for fixed epsilon, and the epsilon→0 limit is a porous-media-type gradient flow with linear error dependence on score error.
Key results
- On CIFAR-10 (padded), FID-based comparison favors deterministic diffusion; Wasserstein distance 27.93 deterministic vs 42.05 stochastic.
- On binary MNIST, Wasserstein distance 15.61 deterministic vs 23.27 stochastic.
- On non-positive 1D distribution, Wasserstein distance 1.953 deterministic vs 3.143 stochastic; deterministic gradient stays bounded while stochastic gradient blows up as t→1.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use deterministic instead of stochastic forward diffusion | Score-based diffusion · 1D compact-support distribution | Wasserstein distance: 3.143 -> 1.953 | Helped |
| Use deterministic instead of stochastic forward diffusion | Score-based diffusion · 2D compact-support distribution | Wasserstein distance: 4.628 -> 2.057 | Helped |
| Use deterministic instead of stochastic forward diffusion | Score-based diffusion · 1D full-support distribution | Wasserstein distance: 2.290 -> 2.315 | Hurt |
| Use deterministic instead of stochastic forward diffusion | Score-based diffusion · 2D full-support distribution | Wasserstein distance: 3.964 -> 3.873 | Helped |
| Use deterministic instead of stochastic forward diffusion | Score-based diffusion · Binary MNIST | Wasserstein distance: 23.27 -> 15.61 | Helped |
| Use deterministic instead of stochastic forward diffusion | Score-based diffusion · CIFAR-10 | Wasserstein distance: 42.05 -> 27.93 | Helped |
| Use deterministic instead of stochastic forward diffusion | Score-based diffusion · Full-support distributions | generation performance | No clear effect |
| Replace the Gaussian kernel with K1 (ablation) | Deterministic diffusion · 2D compact-support distribution | generation performance | No clear effect |
Surprising findings
- On full-support distributions both methods perform comparably, and in the positive-everywhere 2D case the stochastic method slightly outperforms (3.964 vs 3.873 is deterministic better; 2D positive case deterministic 3.873 vs stochastic 3.964).
Limitations
- Long-term convergence for fixed epsilon is not known; theory relies on epsilon→0 limit and porous media equation.
- Theoretical error bound assumes uniformly Lipschitz scores and compact support of rho(t), which may not hold in practice.
- Experiments are small-scale (4-layer MLP on toy and modified image data); FID on CIFAR-10 is reported only qualitatively in text.
Experimental setup
Datasets: synthetic 1D and 2D compactly supported distributions binary MNIST CIFAR-10
Benchmarks: binary MNIST CIFAR-10 (modified, padded to 40x40) synthetic 1D/2D compact-support distributions
Metrics: FID Wasserstein distance gradient norm
Baselines: stochastic diffusion forward process (Song et al. 2020)
Builds on: score-based generative modeling (Song et al. 2020) blob method for diffusions (Carrillo et al. 2019) probabilistic ODE flow Chen, Lee, and Lu 2023 early stopping analysis
Closest papers by meaning
- Accelerating Convergence of Score-Based Diffusion Models, Provably (ICML 2024 · similarity 0.91)
- One-Step Diffusion Distillation through Score Implicit Matching (NeurIPS 2024 · similarity 0.90)
- Unified Convergence Analysis for Score-Based Diffusion Models with Deterministic Samplers (ICLR 2025 · similarity 0.89)
- Dimension-free Score Matching and Time Bootstrapping for Diffusion Models (NeurIPS 2025 · similarity 0.89)
- Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis (ICLR 2025 · similarity 0.89)
- Beyond Scores: Proximal Diffusion Models (NeurIPS 2025 · similarity 0.89)
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.