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Differentiable Solver Search for Fast Diffusion Sampling
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Proposes a differentiable solver search that optimizes timesteps and solver coefficients (not interpolation form) for ODE-based diffusion sampling, reaching 2.33–2.40 FID on ImageNet-256 in 10 steps.
Problem
Fast sampling of pre-trained diffusion and rectified-flow models under very limited numbers of function evaluations; existing Adams-like multistep solvers use hand-crafted t-related Lagrange interpolation that is argued to be suboptimal.
Approach
Pre-integrating the interpolation reduces it to a set of coefficients; the search space is then timesteps plus solver coefficients, optimized differentiably with MSE trajectory alignment to an L-step Euler reference trajectory, with an expectation-based coefficient replacement justified by an error bound.
Key results
- Searched solver with SiT-XL/2 reaches 2.40 FID on ImageNet-256 in 10 steps (with CFG 1.375), and FlowDCN-XL/2 reaches 2.35 FID in 10 steps.
- DiT-XL/2 with the searched solver reaches 2.33 FID in 10 steps, versus 2.79 for the best UniPC/DPM-Solver++ opt variants at 10 steps.
- On ImageNet-512 with DiT-XL/2, the searched solver gives 3.64 FID at 10 steps, beating DPM-Solver++ and UniPC by a large margin.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| search solver coefficients and timesteps | DiT-XL/2 · ImageNet 256×256, 10 steps | FID: 2.79 -> 2.33 | Helped |
| apply the 256×256-searched solver at 512×512 | DiT-XL/2 · ImageNet 512×512, 10 steps | FID: 3.81 -> 3.64 | Helped |
| use the searched solver | PixArt at 512 resolution · GenEval, 8 steps, CFG 2.0 | Overall: 0.44134 -> 0.45064 | Helped |
| search solver coefficients and timesteps | SiT-XL/2 · ImageNet 256×256, 10 steps | FID: 2.27 -> 2.40 | Mixed |
| search solver coefficients and timesteps | FlowDCN-XL/2 · ImageNet 512×512, 10 steps | FID: 2.81 -> 2.77 | Helped |
| combine distillation with solver search | Stable Diffusion v1.5 · COCO-2017 validation, 4 steps | FID: 20.64 -> 18.99 | Helped |
| combine LoRA, distillation, and solver search | SDXL · COCO-2014, 4 steps | FID: 19.32 -> 11.4 | Helped |
| use different search model architectures and sizes (ablation) | SiT-XL/2 solver · SiT-XL/2 FID | FID | Mixed |
| increase reference trajectory step count (ablation) | SiT-XL/2 solver searched with FlowDCN-B/2 · SiT-XL/2 | FID | Helped |
| use 10000 rather than 20000 search samples (ablation) | FlowDCN-B/2 searched solver · SiT-XL/2, 10-step solver | FID: 2.38 -> 2.54 | Hurt |
| use 30000 rather than 20000 search samples (ablation) | FlowDCN-B/2 searched solver · SiT-XL/2, 10-step solver | FID: 2.38 -> 2.49 | Hurt |
| use 40000 rather than 20000 search samples (ablation) | FlowDCN-B/2 searched solver · SiT-XL/2, 10-step solver | FID: 2.38 -> 2.29 | Helped |
Surprising findings
- Solver searched on FlowDCN-B/2 outperformed the solver searched on SiT-XL/2 itself when evaluated on SiT-XL/2, and FID improvements did not track reconstruction error.
- With an optimized high-order solver, DDPM (DiT-XL/2) performance is comparable to rectified flow under similar NFE, contrary to common belief.
Limitations
- Performance degrades with larger classifier-free guidance scales; the solver structure is naive and lacks predictor-corrector.
- Searched solvers are specific to a noise schedule and pre-trained model, so they do not transfer across different beta schedules (e.g., SD1.5).
- Reconstruction error is misaligned with FID, and a search step is still required.
Experimental setup
Datasets: ImageNet-256x256 (via generated samples from pre-trained models)
Benchmarks: ImageNet-256x256 ImageNet-512x512 COCO-2017 COCO-2014 GenEval
Metrics: FID sFID IS precision recall GenEval overall
Baselines: DPM-Solver++ UniPC Adams2 Adams4 Heun FlowTurbo Euler
Builds on: Adams-Bashforth multistep method DPM-Solver++ UniPC
Closest papers by meaning
- A Unified Sampling Framework for Solver Searching of Diffusion Probabilistic Models (ICLR 2024 · similarity 0.91)
- Distilling ODE Solvers of Diffusion Models into Smaller Steps (CVPR 2024 · similarity 0.90)
- Fast ODE-based Sampling for Diffusion Models in Around 5 Steps (CVPR 2024 · similarity 0.90)
- Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Linear Extrapolation (NeurIPS 2025 · similarity 0.89)
- S4S: Solving for a Fast Diffusion Model Solver (ICML 2025 · similarity 0.89)
- Accelerating Diffusion Sampling with Optimized Time Steps (CVPR 2024 · similarity 0.89)
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