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Optimizing for the Shortest Path in Denoising Diffusion Model
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Proposes ShortDF, a DDIM-based diffusion training method that frames denoising as a shortest-path problem and optimizes the initial residual via a relaxation loss, reducing sampling steps while improving FID on CIFAR-10, CelebA, and LSUN Churches.
Problem
Diffusion models need many sampling steps for high quality; fast samplers and distillation methods trade off quality against speed, especially at very few steps.
Approach
Treats the reverse diffusion process as a step-reverse graph and applies shortest-path relaxation to the initial residual |R(t,0)|, adding a loss that acts like a shortcut edge from step t to 0, trained with a base/EMA/graph model triple.
Key results
- On CIFAR-10, ShortDF with 2 steps reaches FID 9.08 versus DDIM's 11.14 at 10 steps (18.5% better, 5.0x speed-up).
- At 10 steps on CIFAR-10, ShortDF achieves FID 3.75, better than gDDIM (DDPM) at 4.17.
- On CelebA at 20 steps, ShortDF reports FID 3.25 versus DDIM's 4.66.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace DDIM sampling with ShortDF | DDIM · CIFAR-10 | FID: 11.14 -> 9.08 | Helped |
| Use ShortDF instead of DDIM | DDIM · CelebA, 10 steps | FID: 10.59 -> 5.00 | Helped |
| Use ShortDF instead of DDIM | DDIM · Churches, 10 steps | FID: 21.52 -> 11.78 | Helped |
| Add shortest-path graph modeling and its loss to DDIM (ablation) | DDIM · Not reported | Not reported | No clear effect |
Surprising findings
- ShortDF at 1 step reports FID 25.07 on CIFAR-10, and on Churches it is worse than DPM-solver++ at 5 steps? No: it is slightly higher than DPM-solver++ at 5 steps (40.38 vs 47.18 favors ShortDF), so the claim of being slightly lower than DPM-Solver++ at 5 steps is inconsistent with the table.
Limitations
- Theoretical framing relies on heuristic graph analogy; the paper admits explicit graph construction and derivation are challenging.
- Evaluation limited to FID on three datasets at low resolution; no text-to-image results despite claims of cross-domain robustness.
- Some reported comparisons are inconsistent with the text (e.g., Churches claim vs. table values).
Experimental setup
Datasets: CIFAR-10 CelebA LSUN Churches
Benchmarks: CIFAR-10 CelebA LSUN Churches
Metrics: FID step time (ms) speed-up
Baselines: DDIM DPM-solver DPM-solver++ iPNDM DEIS D-ODE SDDPM ResFusion gDDIM PNDM RDDM
Builds on: DDPM DDIM DPM-Solver gDDIM
Closest papers by meaning
- Interpreting and Improving Diffusion Models from an Optimization Perspective (ICML 2024 · similarity 0.90)
- Denoising Diffusion Path: Attribution Noise Reduction with An Auxiliary Diffusion Model (NeurIPS 2024 · similarity 0.89)
- Denoising Diffusion Bridge Models (ICLR 2024 · similarity 0.89)
- Residual Denoising Diffusion Models (CVPR 2024 · similarity 0.88)
- Diffusion Bridge Implicit Models (ICLR 2025 · similarity 0.88)
- Score-Optimal Diffusion Schedules (NeurIPS 2024 · similarity 0.88)
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