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Learning to Discretize Denoising Diffusion ODEs
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Proposes LD3, a lightweight method that learns time discretization for diffusion ODE samplers by backpropagating a soft-teacher-forcing LPIPS loss through the solver, without retraining the denoising network.
Problem
Diffusion probabilistic model sampling needs many neural function evaluations; the choice of time discretization strongly affects ODE-solver sample quality at low NFE, and existing schedule optimizers are slow, heuristic, or ignore the solver/network.
Approach
Learn discretization time steps by minimizing a relaxed global truncation error: the student solver may use a nearby perturbed starting point within an r-ball, optimized with projected SGD and LPIPS against teacher outputs, giving a provable KL bound and fast training with no network retraining.
Key results
- On AFHQv2 at NFE=4, iPNDM [LD3] reaches FID 9.96 versus best baseline 12.89.
- At NFE=10, LD3 reaches FID 2.38 on CIFAR10 and 2.27 on AFHQv2 (teacher 2.08 and 2.11).
- On InstaFlow at NFE=2, LD3 improves FID from 22.56 to 15.49.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Learn solver-specific time discretization with LD3 | iPNDM on CIFAR10 · CIFAR10, NFE=4 | FID: 35.04 -> 9.31 | Helped |
| Learn solver-specific time discretization with LD3 | iPNDM on AFHQv2 · AFHQv2, NFE=4 | FID: 12.89 -> 9.96 | Helped |
| Learn time discretization with LD3 | InstaFlow · InstaFlow, NFE=2 | FID: 22.56 -> 15.49 | Helped |
| Use soft teacher forcing instead of hard teacher forcing (ablation) | LD3 on CIFAR10 with decoupled time steps · CIFAR10, NFE=6 | FID: 13.46 -> 7.51 | Helped |
| Add decoupled time-step parameters (ablation) | LD3 on CIFAR10 with soft teacher forcing · CIFAR10, NFE=6 | FID: 12.03 -> 7.51 | Helped |
| Use soft teacher forcing instead of hard teacher forcing (ablation) | LD3 on CIFAR10 without decoupled time steps · CIFAR10, NFE=6 | FID: 14.20 -> 12.03 | Helped |
| Replace LPIPS with L2 loss (ablation) | LD3 on CIFAR10 · CIFAR10, NFE=6 | FID: 7.51 -> 11.78 | Hurt |
| Train discretization using DPM_Solver++ but sample with Euler rather than the matching solver (ablation) | LD3 on AFHQv2 · AFHQv2, NFE=4, Euler sampling | FID: 25.28 -> 42.44 | Hurt |
| Learn time discretization with LD3 | DMPG point-cloud generation · ShapeNet airplane, NFE=8 | CD-COV: 46.95 -> 47.12 | Helped |
| Learn time discretization with LD3 | DiffDock · Molecular docking, NFE=6 | Top-1 RMSD: %<2Å: 32.77 -> 35.31 | Helped |
Surprising findings
- Optimized time steps for DPM-Solver++ transfer poorly to Euler and vice versa, so discretization must be tailored to the solver.
- Naive hard teacher forcing (L_hard) underfits; relaxing to a perturbed-start ball (soft teacher forcing) gives large FID gains (e.g., 13.46 to 7.51 on CIFAR10 at NFE=6).
Limitations
- Still falls short of distillation-based methods in sample quality at very few steps.
- Must be retrained separately for each NFE setting.
- Requires a differentiable ODE solver.
Experimental setup
Datasets: CIFAR10 FFHQ AFHQv2 LSUN-Bedroom ImageNet MS-COCO ShapeNet
Benchmarks: CIFAR10 AFHQv2 FFHQ LSUN-Bedroom ImageNet MS-COCO ShapeNet airplane point cloud PDBbind docking
Metrics: FID MMD COV JSD RMSD <2A success rate
Baselines: Time Uniform Time Quadratic Time EDM Time logSNR DMN GITS AYS
Builds on: DPM-Solver++ UniPC iPNDM AYS DMN GITS
Closest papers by meaning
- PFDiff: Training-Free Acceleration of Diffusion Models Combining Past and Future Scores (ICLR 2025 · similarity 0.91)
- Enhanced Diffusion Sampling via Extrapolation with Multiple ODE Solutions (ICLR 2025 · similarity 0.91)
- Accelerating Diffusion Sampling with Optimized Time Steps (CVPR 2024 · similarity 0.91)
- Score-Optimal Diffusion Schedules (NeurIPS 2024 · similarity 0.91)
- Align Your Steps: Optimizing Sampling Schedules in Diffusion Models (ICML 2024 · similarity 0.91)
- On Inference Stability for Diffusion Models (AAAI 2024 · similarity 0.91)
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