Research map / Image generation / Fast diffusion sampling
Tackling the Singularities at the Endpoints of Time Intervals in Diffusion Models
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 SingDiffusion, a plug-and-play initial-step module that replaces the Gaussian sampling at t=1 with an x-prediction U-Net to fix the average brightness issue and improve FID of pretrained diffusion models.
Problem
Diffusion models assume a Gaussian reverse process, which is not rigorously justified at the singular endpoints t=0 and t=1; ignoring these singularities causes an average brightness problem that prevents generating very bright or dark images.
Approach
Derives error bounds for the Gaussian reverse-process approximation, shows the t=1 singularity is removable and the t=0 one is inherent, and then trains a text-conditioned x-prediction U-Net to estimate the mean image at t=1, used only for the first sampling step before any pretrained model continues sampling.
Key results
- On COCO without guidance, SD-1.5 FID drops from 31.86 to 21.09 with SingDiffusion, and SD-2.0-base FID drops from 25.17 to 18.01.
- For the prompt 'solid black background', SD-2.0-base average brightness goes from 99.67 to 0.29 with SingDiffusion.
- SingDiffusion yields lower FID than SD-1.5 at matched CLIP scores across guidance scales 1.5-8 on COCO.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add SingDiffusion | SD-1.5 · Solid white background | average brightness: 141.43 -> 212.59 | Helped |
| Add SingDiffusion | SD-2.0-base · Solid white background | average brightness: 150.52 -> 227.43 | Helped |
| Add SingDiffusion | SD-1.5 and SD-2.0-base · Solid black background and monochrome line-art logo on a black background | average brightness: 83.09 -> 3.04; 99.67 -> 0.29; 113.66 -> 11.52; 104.45 -> 10.87 | Helped |
| Add SingDiffusion | SD-1.5 and SD-2.0-base · Monochrome line-art logo on a white background | average brightness: 137.95 -> 223.68; 136.13 -> 228.68 | Helped |
| Add SingDiffusion | SD-1.5 · COCO 30k images, without classifier guidance | FID: 31.86 -> 21.09 | Helped |
| Add SingDiffusion | SD-1.5 · COCO 30k images, without classifier guidance | CLIP score: 26.70 -> 27.71 | Helped |
| Add SingDiffusion | SD-2.0-base · COCO 30k images, without classifier guidance | FID: 25.17 -> 18.01 | Helped |
| Add SingDiffusion | SD-2.0-base · COCO 30k images, without classifier guidance | CLIP score: 27.48 -> 28.23 | Helped |
| Add guidance normalization at the initial singular time step (ablation) | SingDiffusion · SD-1.5 across guidance scales [1.5, 2, 3, 4, 5, 6, 7, 8] | FID | Helped |
Surprising findings
- Sampling from a standard Gaussian at t=1-epsilon is equivalent to generating images with average brightness 0, which explains the gray-tone bias of pretrained models.
- The t=0 singularity is argued to be an inherent property that should not be avoided rather than removed.
Limitations
- Relies on a single text-conditioned U-Net trained once, with the mean image estimate amortized over text rather than timestep.
- Guidance normalization is a heuristic that is required to avoid overflow at large guidance scales.
Experimental setup
Datasets: Laion2B-en COCO
Benchmarks: COCO 30k prompts (FID, CLIP score)
Metrics: FID CLIP score average brightness
Baselines: Stable Diffusion 1.5 Stable Diffusion 2.0-base offset noise v-prediction zero terminal SNR
Builds on: DDPM DDIM classifier-free guidance Imagen-style Pareto evaluation offset noise v-prediction
Closest papers by meaning
- Lipschitz Singularities in Diffusion Models (ICLR 2024 · similarity 0.89)
- Diffusion Model is Effectively Its Own Teacher (CVPR 2025 · similarity 0.87)
- Optimizing Quantized Diffusion Models via Distillation with Cross-Timestep Error Correction (AAAI 2025 · similarity 0.87)
- One-step Diffusion with Distribution Matching Distillation (CVPR 2024 · similarity 0.86)
- O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions (ICLR 2025 · similarity 0.86)
- Diffusion models for Gaussian distributions: Exact solutions and Wasserstein errors (ICML 2025 · similarity 0.86)
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.