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Bespoke Non-Stationary Solvers for Fast Sampling of Diffusion and Flow Models
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Proposes Bespoke Non-Stationary (BNS) solvers, a tiny-parameter solver distillation method that optimizes a general non-stationary ODE solver per pretrained diffusion/flow model to maximize PSNR at low NFE.
Problem
Sampling diffusion and flow models requires many sequential function evaluations; model distillation is costly and can reduce diversity, while existing dedicated and solver-distillation approaches are limited in expressiveness and sample fidelity at low NFE.
Approach
Define a Non-Stationary solver family where each step is a learned linear combination of all previous states and velocities, prove it subsumes RK, multistep, exponential, and Scale-Time solvers, and optimize its parameters (about n(n+5)/2+1 values) with a PSNR loss against adaptive RK45 ground-truth trajectories, initialized from Euler or Midpoint with optional scheduler preconditioning.
Key results
- On ImageNet-64 FM-OT, BNS with 16 NFE reaches about 45.6 PSNR and 1.78 FID, versus RK-Midpoint's much lower PSNR at the same NFE, and the paper reports PSNR gains of at least 5-10 dB over the runner-up baseline.
- On text-to-image 512 FM-OT (guidance 2.0), BNS at 16 NFE attains 29.13 PSNR versus 12 to 16 PSNR for RK-Midpoint at 16 NFE (16.28).
- Versus Progressive Distillation on ImageNet-64 (unguided), BNS at 8-16 NFE reaches comparable FID (3.90 at 8 NFE, 2.62 at 16 NFE vs PD 3.39 and 2.97) using about 0.5% of PD's forward passes and 52-168 parameters.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| optimize the generic sampler as a BNS solver (ablation) | FM-OT T2I · MS-COCO val, CFG 2.0, NFE 16 | PSNR: 20.55 -> 29.13 | Helped |
| optimize the generic sampler as a BNS solver (ablation) | FM-OT T2I · MS-COCO val, CFG 6.5, NFE 16 | PSNR: 18.38 -> 21.23 | Helped |
| optimize the generic sampler as a BNS solver (ablation) | FM-OT T2I · MS-COCO val, CFG 2.0, NFE 16 | Pick Score: 20.78 -> 20.90 | Helped |
| optimize the generic sampler as a BNS solver (ablation) | FM-OT T2I · MS-COCO val, CFG 6.5, NFE 16 | Pick Score: 20.87 -> 21.03 | Helped |
| replace Progressive Distillation with BNS | FM-OT · ImageNet-64, NFE 16 | FID: 2.97 -> 2.62 | Helped |
| replace Progressive Distillation with BNS | FM-OT · CIFAR10, NFE 8 | FID: 2.57 -> 2.73 | Hurt |
| replace Progressive Distillation with BNS | FM-OT · ImageNet-64, NFE 8 | FID: 3.39 -> 3.90 | Hurt |
| use BNS instead of the runner-up solver | ImageNet-64 FM-OT · ImageNet-64, NFE 16 | PSNR: +5-10dB | Helped |
| use BNS instead of baselines | Speech FM-OT · Audio generation, across eight datasets | SNR: 1dB-3dB | Helped |
| use BNS instead of Euler | Speech FM-OT · Audiocaps, NFE 8 | WER: 3.49 -> 3.98 | Hurt |
| use BNS instead of Euler | Speech FM-OT · Audiocaps, NFE 8 | speaker similarity: 0.387 -> 0.391 | Helped |
| optimize within the Non-Stationary family rather than the Scale-Time family (ablation) | ImageNet-64 FM-OT · Class-conditional image generation | PSNR | Helped |
Surprising findings
- BNS at 8-16 NFE on ImageNet-64 reports FID (2.62 at 16 NFE) slightly better than Progressive Distillation's 2.97 at 16 NFE in the unguided setting, despite far fewer parameters and forward passes.
Limitations
- Does not reach extremely low NFE regime (1-4), where PD remains better on FID.
- A separate solver must be optimized for each NFE value.
- For text-to-image, relies on classifier-free guidance, which doubles effective batch size; conditional guidance is not incorporated into the solver.
Experimental setup
Datasets: ImageNet-64 (face-blurred) ImageNet-128 (face-blurred) MS-COCO CIFAR10 LibriSpeech CommonVoice v13.0 Switchboard Expresso Audiocaps Fisher Spotify
Benchmarks: ImageNet-64 ImageNet-128 MS-COCO CIFAR10 LibriSpeech CommonVoice v13.0 Switchboard Expresso Audiocaps Fisher Spotify
Metrics: PSNR FID Pick Score Clip Score SNR WER speaker similarity
Baselines: RK-Euler RK-Midpoint DDIM DPM++ BST (Bespoke Scale-Time) Progressive Distillation DOPRI5 / RK45 ground truth
Builds on: Bespoke Scale-Time solvers DDIM DPM-Solver Progressive Distillation EDM
Closest papers by meaning
- Distilling ODE Solvers of Diffusion Models into Smaller Steps (CVPR 2024 · similarity 0.90)
- Bespoke Solvers for Generative Flow Models (ICLR 2024 · similarity 0.90)
- Simple and Fast Distillation of Diffusion Models (NeurIPS 2024 · similarity 0.89)
- PFDiff: Training-Free Acceleration of Diffusion Models Combining Past and Future Scores (ICLR 2025 · similarity 0.88)
- S4S: Solving for a Fast Diffusion Model Solver (ICML 2025 · similarity 0.88)
- Fast ODE-based Sampling for Diffusion Models in Around 5 Steps (CVPR 2024 · similarity 0.88)
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