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Diffusion Sampling with Momentum for Mitigating Divergence Artifacts
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Proposes Heavy Ball momentum and Generalized Heavy Ball (GHVB) modifications to diffusion ODE solvers to enlarge stability regions and suppress divergence artifacts in low-step sampling, training-free.
Problem
High-order diffusion ODE/SDE numerical solvers produce divergence artifacts (oversaturated pixels) when sampling with few steps, because their small stability regions let solutions diverge, limiting achievable acceleration.
Approach
Apply Polyak's Heavy Ball momentum to existing diffusion numerical methods (HB) to enlarge their stability regions with first-order convergence, and generalize HB to high-order Adams-Bashforth-style methods (GHVB) whose momentum number trades accuracy against artifact suppression.
Key results
- On DiT-XL with ImageNet 256, GHVB 3.8 and 3.9 improve FID over PLMS4 when sampling steps are below 10.
- HB momentum applied to DPM-Solver++ and LTSP on ADM improves FID, with HB on LTSP giving the lowest FID scores.
- Numerical order of convergence measured for GHVB 0.5 and GHVB 1.5 approaches 0.5 and 1.5 as steps increase, supporting the theory.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add HB momentum to PLMS4 or DPM-Solver++ | PLMS4 and DPM-Solver++ · Anything V4 text-to-image sampling | latent magnitude score | Helped |
| Reduce the GHVB momentum number (ablation) | GHVB · Anything V4 text-to-image sampling | latent magnitude score | Helped |
| Add HB momentum to DPM-Solver++ | DPM-Solver++ · ADM classifier-guided sampling | FID | Helped |
| Use HB momentum instead of regular Euler for LTSP's second subproblem | LTSP · ADM classifier-guided sampling | FID | Helped |
| Use GHVB 3.8 or GHVB 3.9 instead of PLMS4 | PLMS4 · DiT latent-based diffusion, especially fewer than 10 sampling steps | FID | Helped |
| Use HB 0.9 with PLMS4 | PLMS4 · DiT latent-based diffusion | FID | Helped |
| Use HB 0.8 with PLMS4 (ablation) | PLMS4 · DiT latent-based diffusion | FID | Hurt |
| Use HB or GHVB at high sampling-step counts | PLMS4 · DiT latent-based diffusion, high sampling steps | FID | No clear effect |
| Vary the GHVB damping coefficient (ablation) | GHVB · Stable Diffusion 1.5; latent-space convergence error against 1,000-step PLMS4 | mean L2 distance | Mixed |
| Use GHVB 0.5 and GHVB 1.5 at increasing sampling steps (ablation) | GHVB · Stable Diffusion 1.5; numerical convergence order | order of convergence | Helped |
| Decrease HB's damping coefficient to increase momentum (ablation) | HB-modified numerical methods · Text-to-image sampling with low steps and high guidance | divergence artifacts | Helped |
| Decrease HB's damping coefficient from 1 (ablation) | HB-modified numerical methods · Image quality against 1,000-step DDIM | image quality | Hurt |
Surprising findings
- HB momentum with first-order accuracy still outperforms higher-order PLMS4 at low step counts because artifact suppression matters more than convergence order.
Limitations
- HB momentum drops to first-order convergence when beta is below 1, which blurs images.
- Higher-order GHVB methods show estimated error too small at large step counts, hindering convergence measurement.
Experimental setup
Datasets: ImageNet 256 COCO
Benchmarks: ImageNet 256
Metrics: FID latent magnitude score L2 distance in latent space numerical order of convergence
Baselines: DPM-Solver++ PLMS4 DDIM LTSP DEIS UniPC
Builds on: DDIM DPM-Solver++ PLMS Polyak heavy ball momentum Adams-Bashforth methods
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