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Generative Modeling with Phase Stochastic Bridge
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Proposes Acceleration Generative Modeling (AGM), a phase-space bridge built from stochastic optimal control that straightens CLD trajectories and enables early data prediction ("sampling-hop") for fast low-NFE image generation.
Problem
Sampling efficiency of velocity-augmented (phase-space) diffusion models such as CLD is limited by curved trajectories and the need to converge to a tractable equilibrium prior, making low-NFE generation costly.
Approach
Derive a phase-space Brownian bridge from linear-quadratic stochastic optimal control with a time-varying diffusion coefficient and non-Gaussian boundary conditions, with a terminal velocity defined as (x1 - xt)/(1 - t); the network predicts a force term whose linear combination with state and velocity yields an early estimate of the clean data (sampling-hop).
Key results
- AGM-ODE reaches FID 2.46 with 50 NFE on unconditional CIFAR-10, versus 2.26 for CLD+EI and 1.84 for EDM at 35 NFE.
- AGM-ODE achieves FID 10.55 with 20 NFE on unconditional ImageNet-64, compared with 12.97 for MFM at 40 NFE.
- At NFE 5 on CIFAR-10, AGM-ODE gets FID 11.93 versus EDM at over 100 and CLD+EI at N/A; at NFE 20 AGM-SDE reaches FID 7.9 versus CLD-SDE above 100 at NFE 20.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use AGM-SDE instead of CLD-SDE with the same SSS sampler | CIFAR-10 generation · CIFAR-10, NFE 20 | FID: >100 -> 7.9 | Helped |
| Use AGM-SDE instead of CLD-SDE with the same SSS sampler | CIFAR-10 generation · CIFAR-10, NFE 50 | FID: 19.93 -> 3.21 | Helped |
| Use AGM-SDE instead of CLD-SDE with the same SSS sampler | CIFAR-10 generation · CIFAR-10, NFE 150 | FID: 2.99 -> 2.68 | Helped |
| Use AGM-SDE instead of CLD-SDE with the same SSS sampler | CIFAR-10 generation · CIFAR-10, NFE 1000 | FID: 2.44 -> 2.46 | Hurt |
| Use AGM-ODE instead of CLD+EI | CIFAR-10 fast sampling · CIFAR-10, NFE 10 | FID: 13.41 -> 4.60 | Helped |
| Use AGM-ODE instead of EDM | CIFAR-10 fast sampling · CIFAR-10, NFE 5 | FID: > 100 -> 11.93 | Helped |
| Use AGM-ODE instead of EDM | CIFAR-10 fast sampling · CIFAR-10, NFE 20 | FID: 2.23 -> 2.60 | Hurt |
| Use AGM-ODE instead of MFM | ImageNet-64 unconditional generation · ImageNet-64, NFE 40 | FID: 12.97 -> 10.10 | Helped |
| Use AGM-ODE instead of CLD+EI | CIFAR-10 unconditional generation · CIFAR-10, ODE, NFE 50 | FID: 2.26 -> 2.46 | Hurt |
Surprising findings
- AGM-SDE at NFE 20 on CIFAR-10 gives FID 7.9 while CLD-SDE exceeds 100, showing large gaps at very low NFE.
- The paper reports its method lags state-of-the-art methods when NFE is sufficient.
Limitations
- Performance lags state-of-the-art methods in regimes with sufficient NFE.
- The loss reweighting and normalizer are admittedly heuristic and possibly not optimal.
- Hyperparameter k of the initial covariance was chosen empirically (k=-0.2).
Experimental setup
Datasets: CIFAR-10 AFHQv2 ImageNet-64 Mixture of Gaussians (toy) Multi-Swiss-Roll (toy)
Benchmarks: CIFAR-10 AFHQv2 ImageNet-64
Metrics: FID NFE
Baselines: CLD EDM FM-OT VP VE DDIM Analytic-DPM MFM VP+EI
Builds on: Critically damped Langevin dynamics bridge matching EDM Symmetric splitting sampler Exponential integrator
Closest papers by meaning
- Stochastic Optimal Control for Diffusion Bridges in Function Spaces (NeurIPS 2024 · similarity 0.90)
- On the Trajectory Regularity of ODE-based Diffusion Sampling (ICML 2024 · similarity 0.90)
- Constrained Generative Modeling with Manually Bridged Diffusion Models (AAAI 2025 · similarity 0.88)
- Diffusion Bridge Implicit Models (ICLR 2025 · similarity 0.88)
- CCS: Controllable and Constrained Sampling with Diffusion Models via Initial Noise Perturbation (NeurIPS 2025 · similarity 0.88)
- Consistency Diffusion Bridge Models (NeurIPS 2024 · similarity 0.88)
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