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Action-Minimization Meets Generative Modeling: Efficient Transition Path Sampling with the Onsager-Machlup Functional
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Repurposes pre-trained diffusion and flow-matching generative models for zero-shot transition path sampling by minimizing the Onsager-Machlup action under the model's induced score-driven dynamics.
Problem
Transition path sampling (finding probable paths between two configurations on an energy landscape) is expensive with current ML and enhanced-sampling methods, which need task-specific training and do not exploit large atomistic datasets or pretrained generative models.
Approach
Interpret the score of a pretrained diffusion or flow-matching model as the drift of a Langevin-type SDE, so high-probability transition paths correspond to minimizers of the Onsager-Machlup action; optimize the frozen-score action by gradient descent with fixed endpoints, with no TPS-specific training.
Key results
- On Müller-Brown, the committor-based transition rate estimate is 1.3e-5 versus a true rate of 5.4e-5.
- On alanine dipeptide, OM optimization with a diffusion model needs about 10K score evaluations per path (~50 min) versus 1M force evaluations (~10 hours) for metadynamics.
- On fast-folding proteins, OM-optimized paths give higher valid-path fraction and lower transition NLL than unbiased MD up to 100 microseconds, and lower JSD than MD up to 50 microseconds.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use OM optimization with a pretrained diffusion model instead of metadynamics | Alanine dipeptide transition-path sampling · Alanine dipeptide | FF/score evaluations per path: 1M -> 10K | Helped |
| Use OM optimization with a pretrained diffusion model instead of metadynamics | Alanine dipeptide transition-path sampling · Alanine dipeptide | runtime per path: 10 hours -> 50 min | Helped |
| Use OM optimization with a pretrained diffusion model instead of MCMC two-way shooting | Alanine dipeptide transition-path sampling · Alanine dipeptide | FF/score evaluations per path: ≥ 1B -> 10K | Helped |
| Use OM optimization with a pretrained diffusion model instead of MCMC two-way shooting | Alanine dipeptide transition-path sampling · Alanine dipeptide | runtime per path: ≥ 100 hours -> 50 min | Helped |
| Generate training samples from OM-optimized paths | Committor and rate estimation on the 2D Müller-Brown potential · 2D Müller-Brown potential | transition rate: 1.3 × 10^{-5} vs. 5.4 × 10^{-5} | Mixed |
Limitations
- Does not provably sample the full posterior distribution over paths, unlike shooting methods.
- Path diversity relies on stochastic encode-decode of the generative model rather than principled sampling.
Experimental setup
Datasets: Müller-Brown potential samples alanine dipeptide simulation samples fast-folding protein MD (BBA and others, millisecond-scale) tetrapeptide MD simulations
Benchmarks: Müller-Brown potential alanine dipeptide fast-folding proteins (BBA) tetrapeptides
Metrics: transition negative log likelihood fraction of valid paths Jensen-Shannon divergence free energy barrier force field evaluations per path transition rate estimate
Baselines: metadynamics two-way shooting MCMC unbiased MD i.i.d. diffusion samples
Builds on: Onsager-Machlup action denoising diffusion probabilistic models flow matching Boltzmann generators metadynamics
Closest papers by meaning
- Transition Path Sampling with Improved Off-Policy Training of Diffusion Path Samplers (ICLR 2025 · similarity 0.91)
- Generative Modeling of Molecular Dynamics Trajectories (NeurIPS 2024 · similarity 0.91)
- SE(3)-Stochastic Flow Matching for Protein Backbone Generation (ICLR 2024 · similarity 0.89)
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- Atomic Trajectory Modeling with State Space Models for Biomolecular Dynamics (NeurIPS 2026 · similarity 0.89)
- Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Sampling (NeurIPS 2024 · similarity 0.89)
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