FALCON: Few-step Accurate Likelihoods for Continuous Flows
Danyal Rehman, Tara Akhound-Sadegh, Artem Gazizov, Yoshua Bengio, Alexander Tong
TL;DR
FALCON introduces a hybrid training approach for continuous normalizing flows that enables fast, accurate likelihood computation with fewer steps, significantly improving molecular sampling efficiency in statistical physics.
Contribution
FALCON presents a novel hybrid training method that enhances invertibility and likelihood accuracy in continuous flows, enabling rapid and precise molecular sampling.
Findings
FALCON outperforms existing models in molecular Boltzmann sampling.
FALCON is two orders of magnitude faster than comparable CNF models.
FALCON achieves accurate likelihoods with fewer sampling steps.
Abstract
Scalable sampling of molecular states in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann Generators tackle this problem by pairing a generative model, capable of exact likelihood computation, with importance sampling to obtain consistent samples under the target distribution. Current Boltzmann Generators primarily use continuous normalizing flows (CNFs) trained with flow matching for efficient training of powerful models. However, likelihood calculation for these models is extremely costly, requiring thousands of function evaluations per sample, severely limiting their adoption. In this work, we propose Few-step Accurate Likelihoods for Continuous Flows (FALCON), a method which allows for few-step sampling with a likelihood accurate enough for importance sampling applications by introducing a hybrid training objective that encourages…
Peer Reviews
Decision·ICLR 2026 Oral
Overall, the paper is well executed. The background and preliminaries sections are well written and contain sufficient depth; the problem setting is clear, and the proposed solution is well described. Furthermore, the proposed solution itself seems intuitive (although novelty might be limited, as noted below). Finally, the experimental section is extensive and provides clear evidence in favor of the proposed approach. As such, I am generally in favor of accepting the paper for publication based
My primary objection to voting for acceptance of the paper at this time is the similarity of the proposed method to the one presented in Rehmann et al., 2025. This paper has a very similar objective: combining the benefits of CNFs and discrete-time NFs by enforcing approximate invertibility. Additionally, both papers share a very similar set of experiments (Rehmann et al. is, however, slightly more extensive). While the method presented here has, in theory, sufficient novelty to warrant publicat
The results (in particular Figure 2) are impressive and advance the field. Inference time is orders of magnitude faster than traditional CNFs. Scalable Boltzmann generators can enable new direction in molecular modeling - this is an important advance. The paper is well written and the approach is well motivated, both intuitively and mathematically.
Figure 4 is hard to interpret. What are the x's? Does FALCON really have a constant W2 regardless of the number of samples generated? I don't think this figure is clearly illustrating the data as intended. Although the ability to use a larger model is attributed as a strength of the approach, for comparison purposes it would be nice to train a model of similar size to comparative approaches to factor the effect of model size on performance. L_1 is used without introduction (defined in appendix
1. The paper addresses a core unresolved issue in the flow-matching and continuous normalizing flow (CNF) literature — accurate and efficient likelihood computation — using a very novel and conceptually clean idea. The formulation of few-step likelihood estimation through continuous optimization is both original and impactful. 2. The theoretical development is rigorous, with solid mathematical grounding that explains why the surrogate optimization scheme yields unbiased or low-bias likelihood e
Overall, the work is strong and technically solid, but a few aspects could benefit from further clarification or discussion: 1. Since the method still depends implicitly on the invertibility and numerical conditioning of the local Jacobian, it would be important to analyze the behavior when the Jacobian determinant approaches zero, i.e., when the approximate mean velocity field u_theta becomes locally near-singular. Could such regions lead to unstable or biased likelihood estimates? Most practi
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Taxonomy
TopicsGenerative Adversarial Networks and Image Synthesis · Model Reduction and Neural Networks · Lattice Boltzmann Simulation Studies