While normalizing flows have led to significant advances in modeling high-dimensional continuous distributions, their applicability to discrete distributions remains unknown. In this paper, we show that flows can in fact be extended to discrete events---and under a simple change-of-variables formula not requiring log-determinant-Jacobian computations. Discrete flows have numerous applications. We consider two flow architectures: discrete autoregressive flows that enable bidirectionality, allowing, for example, tokens in text to depend on both left-to-right and right-to-left contexts in an exact language model; and discrete bipartite flows that enable efficient non-autoregressive generation as in RealNVP. Empirically, we find that discrete autoregressive flows outperform autoregressive baselines on synthetic discrete distributions, an addition task, and Potts models; and bipartite flows can obtain competitive performance with autoregressive baselines on character-level language modeling for Penn Tree Bank and text8.

Neural posterior estimation methods based on discrete normalizing flows have become established tools for simulation-based inference (SBI), but scaling them to high-dimensional problems can be challenging.

Neural Information Processing Systems http://nips.cc/

We answer major comments from each reviewer below; we'll fix the minor ones. REVIEWER 1: "This paper ranks high in novelty...The experimental results are strong, especially on T ext Some important details are unclear . E.g. what is the base distribution for sampling? REVIEWER 2: "Originality: This paper is the first demonstration of flow-based models to discrete data. As such, the work is fairly novel....That being said, the main technical contribution amounts to...on top of the We agree about simplicity being a benefit.

Next-generation multimodal foundation models capable of any-to-any cross-modal generation and multi-turn interaction will serve as core components of artificial general intelligence systems, playing a pivotal role in human-machine interaction. However, most existing multimodal models remain constrained by autoregressive architectures, whose inherent limitations prevent a balanced integration of understanding and generation capabilities. Although hybrid and decoupling strategies have been explored to address these tasks within unified frameworks separately, their redundant, non-integrated designs limit their applicability to broader scenarios, such as cross-modal retrieval. In this work, we introduce NExT-OMNI, an open-source omnimodal foundation model that achieves unified modeling through discrete flow paradigms. By leveraging metric-induced probability paths and kinetic optimal velocities, NExT-OMNI natively supports any-to-any understanding and generation with enhanced response efficiency, while enabling broader application scenarios through concise unified representations rather than task-decoupled designs. Trained on large-scale interleaved text, image, video, and audio data, NExT-OMNI delivers competitive performance on multimodal generation and understanding benchmarks, while outperforming prior unified models in multi-turn multimodal interaction and cross-modal retrieval, highlighting its architectural advantages as a next-generation multimodal foundation model. To advance further research, we release training details, data protocols, and open-source both the code and model checkpoints.

We introduce InVirtuoGen, a discrete flow generative model for fragmented SMILES for de novo and fragment-constrained generation, and target-property/lead optimization of small molecules. The model learns to transform a uniform source over all possible tokens into the data distribution. Unlike masked models, its training loss accounts for predictions on all sequence positions at every denoising step, shifting the generation paradigm from completion to refinement, and decoupling the number of sampling steps from the sequence length. For \textit{de novo} generation, InVirtuoGen achieves a stronger quality-diversity pareto frontier than prior fragment-based models and competitive performance on fragment-constrained tasks. For property and lead optimization, we propose a hybrid scheme that combines a genetic algorithm with a Proximal Property Optimization fine-tuning strategy adapted to discrete flows. Our approach sets a new state-of-the-art on the Practical Molecular Optimization benchmark, measured by top-10 AUC across tasks, and yields higher docking scores in lead optimization than previous baselines. InVirtuoGen thus establishes a versatile generative foundation for drug discovery, from early hit finding to multi-objective lead optimization. We further contribute to open science by releasing pretrained checkpoints and code, making our results fully reproducible\footnote{https://github.com/invirtuolabs/InVirtuoGen_results}.

We provide a theoretical analysis for end-to-end training Discrete Flow Matching (DFM) generative models. DFM is a promising discrete generative modeling framework that learns the underlying generative dynamics by training a neural network to approximate the transformative velocity field. Our analysis establishes a clear chain of guarantees by decomposing the final distribution estimation error. We first prove that the total variation distance between the generated and target distributions is controlled by the risk of the learned velocity field. We then bound this risk by analyzing its two primary sources: (i) Approximation Error, where we quantify the capacity of the Transformer architecture to represent the true velocity, and (ii) Estimation Error, where we derive statistical convergence rates that bound the error from training on a finite dataset. By composing these results, we provide the first formal proof that the distribution generated by a trained DFM model provably converges to the true data distribution as the training set size increases.

Designing a new drug often means inventing molecules that have never existed before. Chemists represent molecules as graphs, where atoms are the "nodes" and chemical bonds the "edges," capturing their connections. This graph representation expands far beyond chemistry: a social network is a graph of people and friendships, the brain is a graph of neurons and synapses, and a transport system is a graph of stations and routes. From molecules to social networks, graphs are everywhere and naturally capture the relational structure of the world around us. Therefore, for many applications, being able to generate new realistic graphs is a central problem.

Neural Information Processing Systems http://nips.cc/

We answer major comments from each reviewer below; we'll fix the minor ones. REVIEWER 1: "This paper ranks high in novelty...The experimental results are strong, especially on T ext Some important details are unclear . E.g. what is the base distribution for sampling? REVIEWER 2: "Originality: This paper is the first demonstration of flow-based models to discrete data. As such, the work is fairly novel....That being said, the main technical contribution amounts to...on top of the We agree about simplicity being a benefit.