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PFDiff: Training-Free Acceleration of Diffusion Models Combining Past and Future Scores
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Proposes PFDiff, a training-free, orthogonal timestep-skipping sampler that combines past scores (buffered) and future scores (Nesterov-style foresight) to let first-order and higher-order ODE solvers run with far fewer NFE for diffusion models.
Problem
Diffusion probabilistic model sampling requires many denoising steps; existing fast ODE solvers suffer amplified discretization error at low NFE (below ~10), causing quality loss or non-convergence.
Approach
Reuse the noise-network output from a previous timestep as a stand-in for the current score to predict a "springboard" state, then use the score at that springboard (a future score) with a Nesterov-momentum-inspired foresight update to skip further steps and correct first-order solver error, without any training.
Key results
- On ImageNet 64x64 with classifier guidance, PFDiff with DDIM reduces FID from 138.81 (DDIM, 4 NFE) to 16.46.
- On Stable Diffusion (guidance 7.5, MS-COCO2014), PFDiff on DPM-Solver-1 reaches 13.06 FID at 10 NFE versus 16.78 for the baseline; PFDiff with DDIM achieves 4.10 FID on CIFAR10 at 15 NFE, comparable to DDIM's 4.04 at 1000 NFE.
- PFDiff with DPM-Solver-2 on Stable Diffusion drops FID from 135.81 to 31.66 at 10 NFE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add PFDiff to DDIM | DDIM with Guided-Diffusion · ImageNet 64x64 (classifier guidance, s=1.0), NFE 4 | FID: 138.81 -> 16.46 | Helped |
| Add PFDiff to DPM-Solver-1 | DPM-Solver-1 with Stable-Diffusion · MS-COCO2014, guidance scale 7.5, NFE 10 | FID: 16.78 -> 13.06 | Helped |
| Add PFDiff to DPM-Solver-2 | DPM-Solver-2 with Stable-Diffusion · MS-COCO2014, guidance scale 7.5, NFE 10 | FID: 135.81 -> 31.66 | Helped |
| Add PFDiff to Analytic-DDIM | Analytic-DDIM · CIFAR10 (discrete), NFE 4 | FID: 106.86 -> 289.84 | Hurt |
| Add PFDiff to DDIM | DDIM · CIFAR10 (discrete), NFE 15 | FID: 8.80 -> 4.10 | Helped |
| Use only past scores instead of combining past and future scores (ablation) | PFDiff with DDIM · Unconditional and conditional pre-trained DPMs | FID | Mixed |
| Use only future scores instead of combining past and future scores (ablation) | PFDiff with DDIM · Unconditional and conditional pre-trained DPMs | FID | Mixed |
| Use both past and future scores (ablation) | PFDiff with first-order ODE solvers · Unconditional and conditional pre-trained DPMs, especially NFE < 10 | FID | Helped |
| Fix skip parameters to k=2 and h=1 (ablation) | PFDiff-2_1 · Unconditional and conditional pre-trained DPMs, 4~20 NFE | FID | Helped |
| Vary skip parameters k and h (ablation) | PFDiff · Unconditional and conditional pre-trained DPMs | FID | No clear effect |
Surprising findings
- PFDiff with DDIM at 15 NFE on CIFAR10 matches DDIM at 1000 NFE in FID (4.10 vs 4.04).
- Higher-order solvers such as DPM-Solver-2 fail badly at low NFE on Stable Diffusion (184.21 FID at 4 NFE) and PFDiff repairs much of this gap.
Limitations
- Gains are weaker when NFE is large, and the method relies on the observation that scores change slowly across small step sizes.
- Six PFDiff configurations (k, h) are reported as best results; selecting among them requires visual or metric-based inspection.
- The convergence argument relies on assumptions (e.g., mean value theorem for vector-valued integrals approximated via trajectory planarity) that are approximate.
Experimental setup
Datasets: CIFAR10 CelebA 64x64 LSUN-bedroom 256x256 LSUN-church 256x256 ImageNet 64x64 ImageNet 256x256 MS-COCO2014
Benchmarks: CIFAR10 CelebA 64x64 LSUN-bedroom 256x256 LSUN-church 256x256 ImageNet 64x64 ImageNet 256x256 MS-COCO2014
Metrics: FID Inception Score
Baselines: DDIM Analytic-DDIM DPM-Solver-1 DPM-Solver-2 DPM-Solver-3 DPM-Solver++(2M) UniPC DPM-Solver-v3 AutoDiffusion DDPM Analytic-DDPM
Builds on: DDIM DPM-Solver Analytic-DPM Nesterov momentum
Closest papers by meaning
- Accelerating Diffusion Sampling with Optimized Time Steps (CVPR 2024 · similarity 0.92)
- TADA: Improved Diffusion Sampling with Training-free Augmented DynAmics (NeurIPS 2025 · similarity 0.91)
- Learning to Discretize Denoising Diffusion ODEs (ICLR 2025 · similarity 0.91)
- A Unified Sampling Framework for Solver Searching of Diffusion Probabilistic Models (ICLR 2024 · similarity 0.91)
- A Simple Early Exiting Framework for Accelerated Sampling in Diffusion Models (ICML 2024 · similarity 0.91)
- Accelerating Convergence of Score-Based Diffusion Models, Provably (ICML 2024 · similarity 0.91)
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