Boltzmann Generators have emerged as a promising machine learning tool for generating samples from equilibrium distributions of molecular systems using Normalizing Flows and importance weighting. Recently, Flow Matching has helped speed up Continuous Normalizing Flows (CNFs), scale them to more complex molecular systems, and minimize the length of the flow integration trajectories. We investigate the benefits of using Path Gradients to fine-tune CNFs initially trained by Flow Matching, in a setting where the target energy is known. Our experiments show that this hybrid approach yields up to a threefold increase in sampling efficiency for molecular systems, all while using the same model, a similar computational budget and without the need for additional sampling. Furthermore, by measuring the length of the flow trajectories during fine-tuning, we show that Path Gradients largely preserve the learned structure of the flow.

We present STARFlow, a scalable generative model based on normalizing flows that achieves strong performance on high-resolution image synthesis. STARFlow's main building block is Transformer Autoregressive Flow (TARFlow), which combines normalizing flows with Autoregressive Transformer architectures and has recently achieved impressive results in image modeling. In this work, we first establish the theoretical universality of TARFlow for modeling continuous distributions. Building on this foundation, we introduce a set of architectural and algorithmic innovations that significantly enhance the scalability: (1) a deep-shallow design where a deep Transformer block captures most of the model's capacity, followed by a few shallow Transformer blocks that are computationally cheap yet contribute non-negligibly, (2) learning in the latent space of pretrained autoencoders, which proves far more effective than modeling pixels directly, and (3) a novel guidance algorithm that substantially improves sample quality. Crucially, our model remains a single, end-to-end normalizing flow, allowing exact maximum likelihood training in continuous space without discretization. STARFlow achieves competitive results in both class-and text-conditional image generation, with sample quality approaching that of state-of-the-art diffusion models. To our knowledge, this is the first successful demonstration of normalizing flows at this scale and resolution.

While deep neural networks possess the capability to perform semantic segmentation, producing a single deterministic output limits reliability in safety-critical applications caused by uncertainty and annotation variability. To address this, stochastic segmentation models using Conditional Variational Autoencoders (CVAE), Bayesian networks, and diffusion have been explored. However, existing approaches suffer from limited latent expressiveness and interpretability. Furthermore, our experiments showed that models like Probabilistic U-Net rely excessively on high latent variance, leading to posterior collapse. This work propose a novel framework by integrating Gaussian Mixture Model (GMM) with Normalizing Flow (NF) in CVAE for stochastic segmentation. GMM structures the latent space into meaningful semantic clusters, while NF captures feature deformations with quantified uncertainty. Our method stabilizes latent distributions through constrained variance and mean ranges. Experiments on LIDC, Crack500, and Cityscapes datasets show that our approach outperformed state-of-the-art in curvilinear structure and medical image segmentation.

This paper introduces a generative model equivariant to Euclidean symmetries: E(n) Equivariant Normalizing Flows (E-NFs). To construct E-NFs, we take the discriminative E(n) graph neural networks and integrate them as a differential equation to obtain an invertible equivariant function: a continuous-time normalizing flow. We demonstrate that E-NFs considerably outperform baselines and existing methods from the literature on particle systems such as DW4 and LJ13, and on molecules from QM9 in terms of log-likelihood. To the best of our knowledge, this is the first flow that jointly generates molecule features and positions in 3D.

We propose a general purpose Bayesian inference algorithm for expensive likelihoods, replacing the stochastic term in the Langevin equation with a deterministic density gradient term. The particle density is evaluated from the current particle positions using a Normalizing Flow (NF), which is differentiable and has good generalization properties in high dimensions. We take advantage of NF preconditioning and NF based Metropolis-Hastings updates for a faster convergence. We show on various examples that the method is competitive against state of the art sampling methods.

In the policy evaluation steps, the critic is updated to capture the soft Q-function. In the policy improvement steps, the actor is adjusted in accordance with the updated soft Q-function.

Achieving a balance between image quality (precision) and diversity (recall) is a significant challenge in the domain of generative models.

Second, learning the flow model requires sampling from the feasible action space, which is also challenging.