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S4S: Solving for a Fast Diffusion Model Solver
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Learns a data-free, black-box diffusion ODE solver (S4S) by distilling a teacher solver's endpoint outputs with a relaxed input-ball objective, and extends it to S4S-Alt which alternately optimizes solver coefficients and time discretization.
Problem
Sampling diffusion models with very few neural function evaluations (NFEs) is poor with traditional ODE solvers, whose local truncation error control breaks down at large step sizes; training-free sampler design is under-explored in the coefficient dimension.
Approach
Instead of matching local Taylor-expansion accuracy, directly learn solver coefficients (and optionally time steps) to minimize the global error between the student's final sample and a strong teacher solver's sample, using a relaxed objective that allows a perturbed input within a small L2 ball and LPIPS distance.
Key results
- S4S-Alt with 5 NFEs reaches FID 3.73 on CIFAR-10 and 13.26 on MS-COCO (Stable Diffusion v1.4), about 1.5x better than previous training-free ODE methods.
- On CIFAR-10 at 4 NFEs with LD3 schedule, iPNDM-S4S improves FID from 10.93 to 9.30 (S4S gains across all tested schedules and solvers).
- S4S-Alt at 6 NFEs on CIFAR-10 achieves FID 2.67 versus 3.55 for best traditional solver with learned LD3 schedule.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| learn solver coefficients from iPNDM initialization | iPNDM-S4S · CIFAR-10, LD3, NFE=4–8 | FID: 10.93 -> 9.30; 5.40 -> 4.76; 2.75 -> 2.61 | Helped |
| alternatingly optimize solver coefficients and discretization schedule | S4S-Alt · CIFAR-10, NFE=4–8 | FID: 10.93 -> 6.35; 3.55 -> 2.67; 2.75 -> 2.39 | Helped |
| alternatingly optimize solver coefficients and discretization schedule | S4S-Alt · MS-COCO, NFE=4–8 | FID: 20.22 -> 16.05; 12.33 -> 11.17; 11.30 -> 10.68 | Helped |
| increase solver order from 3 to 4 (ablation) | S4S on FFHQ · FFHQ, NFE=4 | FID: 14.24 -> 13.94 | Helped |
| increase solver order from 3 to 6 (ablation) | S4S on FFHQ · FFHQ, NFE=6 | FID: 5.45 -> 6.11 | Hurt |
| jointly optimize coefficients and schedule instead of alternating (ablation) | S4S-Alt · CIFAR-10, NFE=6 | FID: 2.67 -> 3.28 | Hurt |
| enforce coefficient consistency in the single-step solver (ablation) | DPM-Solver-S4S (2S) · FFHQ, logSNR discretization, NFE=4–8 | FID: 66.82 -> 75.82; 34.91 -> 39.14; 24.73 -> 31.69 | Hurt |
Surprising findings
- Enforcing consistency (coefficients summing to 1) in single-step solvers worsens global error performance.
- Higher solver order (e.g., 6) degrades quality for learned LMS solvers due to overfitting and distant-step information.
Limitations
- Only ODE solvers were studied; SDE solvers are left open.
- Learned coefficients depend on the NFE budget and cannot be reused when NFE changes.
- Coefficients are dataset-level rather than sample-level.
Experimental setup
Datasets: CIFAR-10 FFHQ AFHQv2 LSUN-Bedroom ImageNet MS-COCO
Benchmarks: CIFAR-10 ImageNet FFHQ AFHQv2 LSUN-Bedroom MS-COCO
Metrics: FID
Baselines: UniPC iPNDM DPM-Solver-v3 LD3 AMED-Plugin BNS Progressive Distillation Easy Consistency Models Improved Consistency Training
Builds on: DPM-Solver++ iPNDM UniPC LD3 EDM
Closest papers by meaning
- Distilling ODE Solvers of Diffusion Models into Smaller Steps (CVPR 2024 · similarity 0.92)
- A Unified Sampling Framework for Solver Searching of Diffusion Probabilistic Models (ICLR 2024 · similarity 0.91)
- Align Your Steps: Optimizing Sampling Schedules in Diffusion Models (ICML 2024 · similarity 0.90)
- On Accelerating Diffusion-Based Sampling Processes via Improved Integration Approximation (ICLR 2024 · similarity 0.90)
- Adaptive Stochastic Coefficients for Accelerating Diffusion Sampling (NeurIPS 2025 · similarity 0.89)
- Self-Refining Diffusion Samplers: Enabling Parallelization via Parareal Iterations (NeurIPS 2024 · similarity 0.89)
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