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Adjoint Schrödinger Bridge Sampler
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Proposes Adjoint Schrödinger Bridge Sampler (ASBS), an adjoint-matching diffusion sampler that solves general Schrödinger bridge problems with arbitrary (non-memoryless) priors using only energy evaluations, via alternating adjoint and corrector matching.
Problem
Diffusion samplers for Boltzmann distributions given only unnormalized energies are either non-scalable (importance weights) or restricted to memoryless designs with Dirac or limited priors; existing scalable matching methods cannot use non-memoryless base processes.
Approach
Reinterprets SB optimality conditions as an SOC problem with terminal cost log(hat_phi_1/nu) and learns the drift with alternating adjoint matching (self-consistency on model samples) and a corrector matching objective that estimates the corrector gradient, which provably converges via IPF to the SB solution.
Key results
- ASBS consistently outperforms prior diffusion samplers across all synthetic energy functions (DW-4, MW-5, LJ-13, LJ-55).
- On alanine dipeptide, ASBS achieves lowest KL divergence to ground-truth marginals across all five torsion angles.
- Without warm-start, ASBS with harmonic prior matches or surpasses RDKit-warm-started Adjoint Sampling on amortized conformer generation recall.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ASBS instead of prior diffusion samplers | Synthetic energy functions · DW-4, MW-5, LJ-13, LJ-55 | sampling performance | Helped |
| Use ASBS instead of prior methods | Alanine dipeptide · Alanine dipeptide torsion marginals | KL divergence | Helped |
| Use ASBS with a harmonic prior instead of AS | Amortized conformer generation · SPICE and GEOM-DRUGS test sets | recall coverage | Helped |
| Add RDKit warm-start to ASBS (ablation) | ASBS · Amortized conformer generation | recall coverage | Helped |
| Use a harmonic prior instead of a Gaussian prior (ablation) | ASBS · Amortized conformer generation | recall | Helped |
| Use ASBS instead of AS | Amortized conformer generation · SPICE and GEOM-DRUGS test sets | recall | Helped |
| Use importance weighting to address mode-seeking behavior | SOC-based diffusion samplers · Alanine dipeptide | coverage of low-density modes | Helped |
Surprising findings
- Memoryless condition injects significant noise and biases optimization, motivating non-memoryless designs.
- ASBS with a harmonic prior slightly outperforms a Gaussian prior on conformer generation.
Limitations
- Mode-seeking behavior inherent to SOC-based samplers misses some low-density modes (e.g., alanine dipeptide Ramachandran plot).
- Mode collapse not addressed; importance sampling enhancement left for future work.
Experimental setup
Datasets: SPICE GEOM-DRUGS CREST conformers MCMC samples for DW-4/LJ-13/LJ-55 alanine dipeptide MD samples (10^7)
Benchmarks: DW-4 MW-5 LJ-13 LJ-55 alanine dipeptide amortized conformer generation SPICE/GEOM-DRUGS
Metrics: energy W2/KL-style sample metrics KL divergence of torsion angles recall coverage
Baselines: PIS DDS PDDS SCLD LV iDEM Adjoint Sampling RDKit ETKDG
Builds on: Adjoint Sampling Adjoint Matching Iterative Proportional Fitting Sequential Schrödinger Bridge
Closest papers by meaning
- Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matching (ICML 2025 · similarity 0.92)
- Generalized Schrödinger Bridge Matching (ICLR 2024 · similarity 0.90)
- On scalable and efficient training of diffusion samplers (NeurIPS 2025 · similarity 0.89)
- Statistical Analysis of the Sinkhorn Iterations for Two-Sample Schr\"{o}dinger Bridge Estimation (NeurIPS 2025 · similarity 0.89)
- Learning non-equilibrium diffusions with Schrödinger bridges: from exactly solvable to simulation-free (NeurIPS 2025 · similarity 0.89)
- Non-equilibrium Annealed Adjoint Sampler (NeurIPS 2025 · similarity 0.89)
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