# Few-Step Boltzmann Generators via Scalable Likelihood Flow Maps

arXiv: https://arxiv.org/abs/2606.29110 · HTML: https://mlsanity.com/paper/2606.29110/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 54 references that are in the map.
- First posted on arXiv 27 Jun 2026.

## Builds on (most cited first, 30 of 41)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [How to build a consistency model: Learning flow maps via self-distillation](https://mlsanity.com/paper/2505.18825/) (2025)
- [Normalizing Flows are Capable Generative Models](https://mlsanity.com/paper/2412.06329/) (2024)
- [Flow Contrastive Estimation of Energy-Based Models](https://mlsanity.com/paper/1912.00589/) (2019)
- [Estimating High Order Gradients of the Data Distribution by Denoising](https://mlsanity.com/paper/2111.04726/) (2021)
- [Density Ratio Estimation via Infinitesimal Classification](https://mlsanity.com/paper/2111.11010/) (2021)
- [Scalable Equilibrium Sampling with Sequential Boltzmann Generators](https://mlsanity.com/paper/2502.18462/) (2025)
- [Free-form Flows: Make Any Architecture a Normalizing Flow](https://mlsanity.com/paper/2310.16624/) (2023)
- [Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models](https://mlsanity.com/paper/2506.17139/) (2025)
- [Learning normalized image densities via dual score matching](https://mlsanity.com/paper/2506.05310/) (2025)
- [Joint Distillation for Fast Likelihood Evaluation and Sampling in Flow-based Models](https://mlsanity.com/paper/2512.02636/) (2025)
- [BNEM: A Boltzmann Sampler Based on Bootstrapped Noised Energy Matching](https://mlsanity.com/paper/2409.09787/) (2024)

## Built on by (most cited first, 2 of 2)

- [OMatG-flash: An All-Atom Flow Map with Reinforce Adjoint Matching for Scalable Materials Discovery](https://mlsanity.com/paper/2609.26402/) (2026)
- [Grand Canonical Generators](https://mlsanity.com/paper/2610.00683/) (2026)

## Abstract (arXiv)

Recent progress in flow-based generative modeling has led to models that output high-quality samples while using only a small number of function evaluations. However, at present, there is a lack of similar advances in estimating the model likelihood. In particular, most existing methods either rely on restrictive architectures that enable exact calculations, or use stochastic approximations such as Hutchinson's trace estimator that introduce substantial variance. In this work, we introduce SCAlable LikeLihood distillation of flOw maPs (SCALLOP). SCALLOP builds on the recently proposed F2D2, a likelihood flow map model that can generate samples and their densities in a small number of function evaluations. While F2D2 uses Hutchinson's estimator during training, we introduce an alternative and more scalable likelihood distillation objective that is Hutchinson-free and admits a vectorized formulation. Empirically, we demonstrate the effectiveness of SCALLOP as a Boltzmann generator in molecular science, and further validate its benefit on image datasets. SCALLOP significantly reduces both training variance and training time while consistently improving performance compared to F2D2, and is competitive with the state-of-the-art while achieving up to 10x inference speedup over the fastest baseline.