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Efficient Integrators for Diffusion Generative Models
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Proposes Conjugate Integrators and Splitting Integrators (plus their combination) as fast deterministic and stochastic samplers for augmented diffusion models, applied to Phase Space Langevin Diffusion (PSLD) on CIFAR-10.
Problem
Slow sample generation in diffusion models, especially augmented (position-momentum) diffusions like PSLD, which lack efficient samplers at low NFE budgets.
Approach
Conjugate integrators map the probability-flow ODE into an affine-transformed space with a tunable matrix B_t (lambda-DDIM), generalizing DDIM and exponential integrators; splitting integrators borrowed from molecular dynamics alternate position and momentum updates, with reduced-NFE adjustments, and are combined with conjugate integrators.
Key results
- CSPS-D (conjugate splitting Velocity Verlet deterministic sampler) achieves FID 2.11 on CIFAR-10 at 100 NFE, versus 2.57 for the best baseline (DEIS).
- SPS-S (reduced OBA stochastic sampler) achieves FID 2.36 at 100 NFE, versus 2.63 for the best stochastic baseline (SA-Solver).
- At 50 NFE, CSPS-D reaches FID 2.65 with preconditioning (3.21 without), and the best stochastic sampler reaches 2.74.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add score network preconditioning (ablation) | CSPS-D on PSLD · CIFAR-10, NFE=50 | FID: 3.21 -> 2.65 | Helped |
| add score network preconditioning (ablation) | SPS-S on PSLD · CIFAR-10 | FID: 2.76 -> 2.74; 2.36 -> 2.47 | Mixed |
| use reduced splitting adjustments instead of naive splitting (ablation) | deterministic PSLD samplers · CIFAR-10 | FID: 132.45 -> 23.5; 23.47 -> 5.31; 69.06 -> 14.19; 14.49 -> 3.41 | Helped |
| reuse score evaluations and tune position-space noise in OBA (ablation) | stochastic PSLD sampler · CIFAR-10 | FID: 36.87 -> 2.76; 15.18 -> 2.36 | Helped |
| add lambda-DDIM-II conjugacy to reduced deterministic splitting (ablation) | RVV and RSE on PSLD · CIFAR-10 | FID: 14.19 -> 3.21; 3.41 -> 2.11; 23.5 -> 3.92; 5.31 -> 2.68 | Helped |
| add lambda-DDIM-II conjugacy to reduced stochastic splitting (ablation) | ROBA on PSLD · CIFAR-10 | FID: 2.76 -> 2.94; 2.36 -> 2.49 | Hurt |
| use conjugate splitting rather than Euler-based reduced splitting (ablation) | deterministic PSLD sampling · CIFAR-10 | FID: FID scores of 2.65 and 2.11 in 50 and 100 NFEs | Helped |
Surprising findings
- Applying conjugate integrators to the stochastic ROBA sampler slightly degraded sample quality, which the authors attribute to a suboptimal choice of B_t.
- Naive splitting samplers can perform substantially worse than Euler at low NFE, motivating the reduced-splitting adjustments.
Limitations
- Conjugate integrator is restricted to deterministic samplers in the current presentation.
- Choice of the B_t matrix and splitting parameters (e.g., lambda_s) is heuristic and lacks theoretical grounding.
- Conjugate integration did not improve the stochastic splitting sampler, suggesting B_t choice is suboptimal.
Experimental setup
Datasets: CIFAR-10 CelebA-64 AFHQ-v2
Benchmarks: CIFAR-10 CelebA-64 AFHQ-v2
Metrics: FID NFE
Baselines: DDIM DEIS DPM-Solver-3 PNDM EDM gDDIM A-DDIM SA-Solver SEEDS-2 SSCS Euler-Maruyama
Builds on: DDIM Phase Space Langevin Diffusion DEIS EDM
Closest papers by meaning
- On Accelerating Diffusion-Based Sampling Processes via Improved Integration Approximation (ICLR 2024 · similarity 0.88)
- On scalable and efficient training of diffusion samplers (NeurIPS 2025 · similarity 0.88)
- Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics (ICLR 2025 · similarity 0.88)
- Self-Refining Diffusion Samplers: Enabling Parallelization via Parareal Iterations (NeurIPS 2024 · similarity 0.88)
- Wasserstein Convergence of Critically Damped Langevin Diffusions (NeurIPS 2025 · similarity 0.88)
- Accelerating Convergence of Score-Based Diffusion Models, Provably (ICML 2024 · similarity 0.88)
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