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Few-Step Boltzmann Generators via Scalable Likelihood Flow Maps

NeurIPS 2026 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Expressive invertible architectures · 0 citations (OpenAlex)

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Proposes SCALLOP, a Hutchinson-free, vectorized conditional divergence-matching objective for training few-step likelihood flow maps, enabling fast joint sampling and density evaluation for Boltzmann generators on alanine peptides and CelebA-64.

Problem

Few-step flow-map generative models lack scalable, low-variance likelihood evaluation; existing likelihood estimation relies on Hutchinson trace estimators or costly Jacobian log-determinants, which hinders their use as Boltzmann generators.

Approach

Replace the Hutchinson-based divergence distillation in F2D2 with a conditional, vectorized divergence matching objective (CDM-v) derived from the chain rule and conditional time/space scores, so the divergence target is an analytic conditional quantity with no JVP or trace estimation.

Key results

• On ALA-6, SCALLOP achieves the best torsion W2 (1.120 vs 1.143 for F2D2) and roughly halves the energy W2 relative to F2D2 (5.845 vs 10.140) on ALA-6.
• SCALLOP reduces training gradient variance by up to 100x and uses about 10% less training time than F2D2 per update, as it avoids JVPs.
• On CelebA-64 with 1 Euler step, SCALLOP attains BPD error 0.17 vs 0.53 for F2D2 and FID 6.91 vs 6.94.

Surprising findings

• Vanilla flow map without likelihood training yields wildly wrong BPD (e.g., -69.83 at 1 step), showing likelihood must be learned jointly.
• FALCON attains lower energy W2 on several alanine systems than SCALLOP, so SCALLOP does not uniformly dominate state of the art.

Limitations

• CDM objective assumes the velocity field is perfectly learned; the resulting bias is not quantified.
• Practically uses around 10 steps for high-dimensional tasks despite one-step capability.
• Still underperforms FALCON on energy W2 for several alanine systems.

Experimental setup

Datasets: ALA-2 MD data ALA-3 MD data ALA-4 MD data ALA-6 MD data CelebA-64

Benchmarks: ALA-2 ALA-3 ALA-4 ALA-6 CelebA-64

Metrics: ESS energy 2-Wasserstein torsion 2-Wasserstein BPD FID NLL absolute deviation training gradient SNR

Baselines: SBG-IS FALCON FALCON-A F2D2 flow map

Builds on: F2D2 flow map flow matching Lagrangian self-distillation FALCON

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