Discrete Flow Matching

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3 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Jul 13Week of Sep 28

Latest papers 19

Oct 1, 2026cs.LG

pCoMole: Pareto-Constrained Molecule Editing with Discrete Flows

Biomolecular therapeutics often start from known sequences and require targeted editing to improve multiple properties while satisfying hard biochemical and manufacturability constraints. However, existing generative methods do not jointly support multi-objective optimization, hard feasibility, and sequence editing in discrete, variable-length biological spaces. In this work, we introduce Pareto-Constrained Molecule Editing (pCoMole), a framework built on discrete flow matching that steers a pre-trained Edit Flow toward user-specified preferences while enforcing terminal feasibility. pCoMole defines a feasibility-gated terminal distribution using an augmented Tchebycheff utility and realizes the resulting preference tilt through a Doob-h transform of the underlying edit process. To make this construction practical, we approximate the required harmonic function using short Monte Carlo rollouts over candidate edits, yielding an efficient guided editor with provable preference consistency. We validate pCoMole by shrinking GFP while retaining fluorescence-related properties, shortening diverse Cas9 orthologs while preserving PAM specificity, and compressing peptide binders into short peptidomimetics that optimize seven drug-related properties under hard constraints. In wet lab testing, two 229-residue pCoMole-designed eGFP variants retained clear green fluorescence in BL21 cells after 10 deletions, with either one or two substitutions. Together, pCoMole enables constraint-aware, Pareto-aligned editing of biomolecular sequences in discrete, variable-length spaces.

Tong Chen, Maximilian Holsman, Lin Zhao +1

Department of Computer and Information Science, University of Pennsylvania · Department of Computer Science, Duke University · Department of Bioengineering, University of Pennsylvania

Constrained Generative Modeling Protein Design Multi-Objective Optimization Discrete Flow Matching

Oct 1, 2026stat.ML

Zero Flux: Flow-Based Comparison of High-Dimensional Discrete Distributions

Comparing two high-dimensional discrete distributions has always been a challenging task due to the exponentially growing state space and complex changes in interactions. A recent work suggests comparing distributions through a vector field trained using flow matching between two continuous distributions. The resulting vector field at mid-point vanishes if and only if two distributions identical. However, such a flow-based criterion does not naturally apply to discrete distributions. We extend this principle to the discrete domain and introduce the \emph{Zero Flux} criterion, a discrepancy based on local probability fluxes. Under independent coupling, we show that all local probability fluxes vanish at the midpoint if and only if two distributions are the same. This discrepancy decomposes the joint distributional difference into smaller, local contributions and can be efficiently estimated from samples. We establish finite sample error bounds for our estimator. Experiments on synthetic and real categorical data demonstrate reliable recovery of sparse dependence signals and stable tracking of distribution shifts in high dimensions.

Leyang Wang, Yakun Wang, Song Liu +1

Department of Mathematical Informatics, The University of Tokyo, Japan · Center for Advanced Intelligence Project, RIKEN, Japan · School of Mathematics, University of Bristol, United Kingdom

Distribution Shift Distribution Shift Detection Distribution Matching Discrete Flow Matching

Sep 11, 2026cs.LG

Flow Duality and Source Geometry for Categorical Generation

Continuous and discrete flow matching are usually treated as separate constructions. This paper identifies a duality between them: projecting continuous convex-interpolant paths with one-hot targets through a position-wise argmax yields discrete convex-interpolant paths. The result requires source laws with appropriate coordinate symmetry and boundary regularity, and it makes the continuous source distribution an explicit design choice for categorical generation. We derive the induced discrete interpolation behavior for Gaussian, bounded-uniform, and centered negative-exponential sources, showing that different source geometries lead to qualitatively different transition timing and vocabulary-size dependence. Small visual diagnostics and a short language-modeling pilot suggest that these source-design effects can also appear in learned transports and early generative quality.

Etrit Haxholli

Flow Matching Flow-Based Generative Modeling Discrete Flow Matching

Jul 29, 2026cs.LG

Latent-Kernel Discrete Flow Maps for Few-Step Generation

Discrete diffusion and flow-matching models denoise a sequence over many steps, but to keep each step cheap, they factorize the transition across positions and decide every token independently. This makes few-step generation challenging for text when the target couples two positions, such as a subject and a verb that must agree. An independent update commits to them separately, and many function evaluations are spent repairing the mismatch. Existing few-step methods buy back the lost correlation by distilling or rectifying a slow teacher, and so inherit the teacher's quality ceiling. We ask instead whether a model can express correlated steps natively, and answer with Latent-Kernel Discrete Flow Maps (LKF), a from-scratch flow-map kernel that is a mixture of M factorized components tied by a single shared latent. Conditioned on the latent, each component is cheap, and the mixture is summed over the latent in closed form for small M. We show that a single step places mass on correlated completions with the same sampling time complexity as a factorized model, since one latent is drawn per sequence and reused across the entire denoising trajectory. We also show that the Masked Diffusion Language Model (MDLM) is a special case of our LKF model at M=1. The experiments for unconditional text generation on the One-Billion-Word (LM1B) and WikiText-103 benchmarks show that our LKF model learns strongly heterogeneous components and improves generative perplexity by 2.1x to 3.3x over the likelihood baselines without losing diversity. The gain grows with M, and at M=8, it surpasses distilled and rectified few-step samplers. The source code is available at: https://github.com/mansoor181/lkf.git

Mansoor Ahmed, Yue-Tsz Fan, Hemanth Venkateswara +1

Georgia State University, Atlanta, GA, USA · Georgia Institute of Technology, Atlanta, GA, USA

Latent Variable Models Few-Step Diffusion Sampling Flow Map Learning Flow-Based Generative Modeling Diffusion Language Models Discrete Flow Matching

Jul 23, 2026cs.LG

Context-weighted Discrete Flow Matching

Discrete flow matching provides a flexible framework for generative modeling on discrete structures. However, the standard factorized training objective exposes the model to targets of varying difficulty, mixing well-conditioned, predictable tokens with ambiguous, high-entropy ones. We empirically demonstrate that the uncertainty over the value of each token is closely related to the density of available context in its neighborhood. Motivated by this observation, we propose a simple modification to the underlying continuous-time Markov chain (CTMC) that incorporates local context information. Our context-weighted sampler improves generation quality with negligible computational overhead, while our scaled cross-entropy loss function reweights the training signal from different tokens and reduces generative perplexity by up to 63% on OpenWebText. Moreover, our approach matches a strong semi-autoregressive block diffusion baseline in quality while retaining the ability to perform generation in any order. These results highlight the role of local context as an important factor in discrete generative modeling and show that simple context-aware modifications can significantly improve both sampling and training efficiency.

Daniil Cherniavskii, Daniel Severo, Karen Ullrich

University of Amsterdam · Work done during an internship at Meta FAIR. · Meta FAIR

Non-Autoregressive Text Generation Adaptive Loss Weighting Flow-Based Generative Modeling Discrete Flow Matching

Jul 12, 2026cs.GR

LATO.2: Factorized 3D Mesh Generation with Vertex and Topology Flow

Flow matching over carefully designed latent representations has recently emerged as a powerful paradigm for topology-aware mesh generation. Existing approaches, however, model vertices and connectivity jointly in a joint latent space, entangling continuous vertex geometry with discrete combinatorial structure; this complicates flow learning and manifests as drifting vertices and broken surfaces. We present LATO.2, a factorized flow matching framework that decomposes mesh generation into a vertex flow followed by a connectivity flow conditioned on the realized vertices, with both stages anchored to a shared coarse voxel scaffold. Dedicated VAEs underpin the two stages, recovering vertices at sub-voxel precision and embedding discrete connectivity into a continuous latent space. We demonstrate two advantages unique to this factorization: (i) part-wise generation, in which the scaffold is partitioned and each part synthesized at full latent capacity, yielding substantially higher-resolution meshes than a monolithic latent permits; and (ii) topology-adaptive editing, in which manipulating first-stage vertices induces the corresponding connectivity without re-optimization. Experiments show that LATO.2 surpasses state-of-the-art topology-aware mesh generators in geometric fidelity and connectivity quality.

Hang Long, Tianhao Zhao, Junkai Lin +7

Huazhong University of Science and Technology · Meshy AI · Independent Researcher +1

Flow Matching 3D Mesh Generation 3D Shape Generation Discrete Flow Matching

Jul 9, 2026physics.optics

Joint Discrete-Continuous Flow Matching for Open-Vocabulary Inverse Design of Multilayer Optical Coatings

Amortized neural inverse design typically remains closed-world: component choices are fixed vocabulary tokens, coordinate grids are frozen at training time, and continuous variables are discretized into sequence tokens. Multilayer optical coatings are an industrially important instance, coupling material sequence, layer thickness and wavelength-dependent response. We present IrisFlow, a query-based, open-vocabulary flow-matching framework instantiated in coatings: the target reflectance/transmittance spectrum, wavelength grid, candidate-material optical constants and layer count are supplied at query time. Candidate materials enter as wavelength-aware optical tokens rather than learned identities; material sequences are sampled by discrete flow matching over the query's candidate bank, thicknesses by continuous flow matching without discretization. A single 136M-parameter model designs 2-100-layer stacks. Across a 224-task benchmark it reconstructs in-distribution targets faithfully and retains same-order accuracy on a 15-material held-out bank without retraining; it reconstructs bands up to 1100 nm beyond its training envelope, designs against analytic application specifications and outperforms an autoregressive baseline on that baseline's material library. With optical constants calibrated to our deposition process, IrisFlow designs four color-displaying coolers, fabricated by ion-assisted evaporation: the three chromatic devices reach a CIEDE2000 color error of 3.1-5.2 while retaining 93-95% solar near-infrared reflectance, demonstrating open-vocabulary design carried through to fabricated coatings.

Zhiyi Li, Yuheng Jin, Yidan Huang +3

School of Electronic Science and Engineering (National Model Microelectronics College), Xiamen University, Fujian, 361005, China. · 2Fujian Key Laboratory of Ultrafast Laser Technology and Applications, Xiamen University, Xiamen, 361005, China.

Flow Matching Inverse Design Discrete Flow Matching

Jun 28, 2026cs.AI

Flow Reasoning Models: Turning Flows Into Efficient Recurrent Reasoners

Structured reasoning requires making and revising interdependent decisions to reach a globally consistent solution. Existing architectures struggle with this: autoregressive models commit sequentially and cannot revise earlier decisions, while masked diffusion models often require careful decoding schemes to coordinate interdependent predictions. We introduce Flow Reasoning Models (FRMs), a novel framework for structured reasoning that adapts continuous flows over discrete structured outputs with a simple recurrent refinement mechanism. By self-conditioning a flow model on its own past outputs, we turn one-shot denoising into iterative solution refinement. This lets FRMs make and revise decisions in parallel, efficiently coordinating interdependent choices across solutions. Yet conventional self-conditioning becomes unreliable at greater recurrent depth due to exposure bias between one-step training predictions and recursively generated inference states. We address this mismatch with Fixed-Point Forcing (FPF), which trains FRMs on states produced by their own inference dynamics while preserving the standard flow-matching objective. FRMs achieve solve rates of

99.5\%

,

100.0\%

, and

99.9\%

on Sudoku-Extreme, Zebra, and Maze-Unique, respectively. On Sudoku-Extreme, FRMs achieve higher peak accuracy than the evaluated masked-diffusion and specialized reasoning baselines while remaining highly compute-efficient, matching the next-best method's

98.7\%

peak solve rate with

44\times

fewer inference FLOPs.

Alec Helbling, Andrey Bryutkin, Mauro Martino +3

1Georgia Tech · 3MIT-IBM Computing Research Lab · 4IBM Research +1

Structured Reasoning Flow-Based Generative Modeling Constraint Satisfaction Iterative Refinement Algorithmic Reasoning Discrete Flow Matching

Jun 23, 2026cs.LG

A Time-Reparameterized Cumulative Intensity Extrapolation Sampler for Discrete Flow Matching

Discrete flow matching (DFM) provides a principled framework for generative modeling on discrete state spaces via continuous-time Markov chain dynamics. In practice, sampling for DFM commonly employs discretizations such as

τ

-leaping, yet efficient sampling methods under a limited number of function evaluations (NFE) remain less studied. To address this gap, we propose the Time-Reparameterized Cumulative Intensity Extrapolation (TR-CIE) sampler, which aims to improve sampling quality when function evaluations are restricted. TR-CIE consists of two components. First, a schedule-based time reparameterization rescales the time grid according to the noise schedule. Under standard factorized DFM rate parameterizations, this transformation of variables absorbs the schedule-dependent growth term and mitigates stiffness near the terminal sampling stage. Second, we introduce a cumulative-intensity extrapolation updating rule. By reusing cached model outputs from the previous step as a history term, this improves the approximation of stepwise cumulative intensities on the resulting non-uniform time grid. We provide a theoretical analysis that bounds the local approximation error of cumulative intensities and establishes convergence results. The resulting sampler requires one NFE per step and introduces no additional model evaluations compared to the standard

τ

-leaping sampler. Extensive experiments on synthetic tasks, text generation, and text-to-image benchmarks demonstrate that our method improves sampling quality under limited NFE.

Feiyang Fu, Hehe Fan

College of Artificial Intelligence, Zhejiang University, Hangzhou, China.

Flow Matching Few-Step Diffusion Sampling Flow-Based Generative Modeling Discrete Flow Matching

Jun 22, 2026cs.CV

Flow6D: Discrete-to-Continuous Flow Matching for Efficient and Accurate Category-Level 6D Pose Estimation

6D pose estimation is a key task in computer vision and embodied AI, widely used in robotic manipulation, augmented reality, etc. Existing methods directly regress in a high-dimensional continuous space, facing two key challenges in category-level pose estimation: limited accuracy due to noise and local optima, and inefficient search over an infinite space that hinders real-time performance. This paper proposes Flow6D, a hierarchical flow matching framework with a two-stage discrete latent space localization-continuous pose regression strategy. Rotation and translation parameters are first discretized into bins, with a discrete flow matching model locking the latent space around the true pose to reduce search complexity. Then, by sampling in the latent space, a continuous flow matching model predicts local pose residuals to optimize the estimate and regress to an accurate pose. The framework also naturally extends to articulated objects, outperforming state-of-the-art methods on synthetic and real datasets with real-time inference at 70 FPS. Project website: https://flow6d.github.io/.

Mingyu Mei, Li Zhang, Zibo Dai +4

Zhejiang University · University of Science and Technology of China · Shanghai Jiao Tong University

Flow Matching Object Pose Estimation Discrete Flow Matching

Jun 12, 2026cs.SD

Mask, Sample, Revise: A Revisable CTMC Inference Stack for Guided Discrete Flow Matching Text-to-Speech

Recent alignment-free non-autoregressive (NAR) text-to-speech (TTS) models formulate synthesis as a conditional infilling task, bypassing explicit duration predictors and external aligners. When speech is represented with neural codec tokens, the infilling problem becomes discrete, making Discrete Flow Matching (DFM), a Continuous-Time Markov Chain (CTMC) framework for discrete generation, a natural fit. However, inference-time control for stable low-step conditional infilling remains underexplored. We propose Mask, Sample, Revise, an inference-time CTMC stack for alignment-free DFM-TTS. The stack combines predictor-free guidance to strengthen text conditioning, prompt-matched conditional coupling to align the probability path with the acoustic prompt, and SC-ReMask, a schedule-constrained remasking mechanism that introduces token-to-mask transitions so de-masking decisions can be revised. These components require no post-hoc fine-tuning and operate in a single tau-leaping sampler. Controlled ablations show that this stack improves intelligibility and robustness in the low-NFE prompted setting, outperforming unguided and guidance-only samplers with substantially more steps.

Alef Iury Siqueira Ferreira, Lucas Rafael Stefanel Gris, Luiz Fernando de Araújo Vidal +4

Federal University of Goi´as, Goiˆania, Brazil · Federal University of Mato Grosso, Cuiab´a, Brazil · Elsa Speak, S˜ao Paulo, Brazil

Flow Matching TTS Synthesis Flow-Based Generative Modeling Inference-Time Guidance Discrete Flow Matching

Jun 9, 2026cs.LG

Flexible Flows for Biological Sequence Design

Designing functional biological sequences requires navigating vast discrete spaces under strict evolutionary and biophysical constraints. Discrete Flow Matching (DFM) offers a generative framework over such spaces, but existing approaches rely on biologically uninformative couplings and offer limited flexibility for variable-length sequence generation and fine-grained control. We propose a structured coupling that encodes domain-specific preferences among sequence elements, biasing the source distribution toward plausible regions without modifying the flow objective or training procedure. Building on this, we introduce a latent edit-based rate parameterization that models variable-length generation via edit operations conditioned on a shared global latent, akin to a latent variable model, while remaining tractable. We further introduce a latent classifier-free guidance mechanism that steers generation coherently in continuous latent space, along with Dirichlet-prior temperature scaling for test-time control over edit operations. Our method achieves state-of-the-art performance across diverse biological sequence tasks, including density estimation, unconditional and conditional DNA sequence generation, and peptide sequence generation.

Yogesh Verma, Dani Korpela, Harri Lähdesmäki +1

Aalto University, Finland · Aalto University and YaiYai Ltd

Flow Matching Molecular Generation Flow-Based Generative Modeling Conditional Generative Modeling Sequence Modeling Discrete Flow Matching

May 12, 2026cs.LG

Discrete Flow Matching for Offline-to-Online Reinforcement Learning

Many reinforcement learning (RL) tasks have discrete action spaces, but most generative policy methods based on diffusion and flow matching are designed for continuous control. Meanwhile, generative policies usually rely heavily on offline datasets and offline-to-online RL is itself challenging, as the policy must improve from new interaction without losing useful behavior learned from static data. To address those challenges, we introduce DRIFT, an online fine-tuning method that updates an offline pretrained continuous-time Markov chain (CTMC) policy with an advantage-weighted discrete flow matching loss. To preserve useful pretrained knowledge, we add a path-space penalty that regularizes the full CTMC trajectory distribution, rather than only the final action distribution. For large discrete action spaces, we introduce a candidate-set approximation that updates the actor over a small subset of actions sampled from reference-policy rollouts and uniform exploration. Our theoretical analysis shows that the candidate-set error is controlled by missing target probability mass, and the induced CTMC generator error decreases as the candidate set covers more high-probability actions. Experiments on prevailing discrete action RL task show that our method provides stable offline-to-online improvement across all tasks, achieving the highest average score on Jericho with a simple GRU encoder while outperforming methods that use pretrained language models. Controlled experiments further confirm that the path-space penalty remains bounded during fine-tuning and that the CTMC generator adapts to shifted rewards faster than deterministic baselines. The candidate-set mechanism is supported by a stability analysis showing that the generator error decreases exponentially with candidate coverage.

Fairoz Nower Khan, Nabuat Zaman Nahim, Peizhong Ju

Department of Computer Science, University of Kentucky

Flow Matching Reinforcement Learning RL Fine-Tuning Offline-To-Online RL Discrete Flow Matching

May 10, 2026eess.AS

Kinetic-Optimal Scheduling with Moment Correction for Metric-Induced Discrete Flow Matching in Zero-Shot Text-to-Speech

Metric-induced discrete flow matching (MI-DFM) exploits token-latent geometry for discrete generation, but its practical use is limited by two issues: heuristic schedulers requiring hyperparameter search, and finite-step path-tracking error from its first-order continuous-time Markov chain (CTMC) solver. We address both issues. First, we derive a kinetic-optimal scheduler for prescribed scalar-parameterized probability paths, and instantiate it for MI-DFM as a training-free numerical schedule that traverses the path at constant Fisher-Rao speed. Second, we introduce a finite-step moment correction that adjusts the jump probability while preserving the CTMC jump destination distribution. We validate the resulting method, GibbsTTS, on codec-based zero-shot text-to-speech (TTS). Under controlled comparisons with a unified architecture and large-scale dataset, GibbsTTS achieves the best objective naturalness and is preferred in subjective evaluations over masked discrete generative baselines. Additionally, in comparison with the evaluated state-of-the-art TTS systems, GibbsTTS shows strong speaker similarity, achieving the highest similarity on three of four test sets and ranking second on the fourth. Project page: https://ydqmkkx.github.io/GibbsTTSProject

Dong Yang, Yiyi Cai, Haoyu Zhang +2

1The University of Tokyo · 2Independent Researcher

Flow Matching TTS Synthesis Zero-Shot TTS Flow-Based Generative Modeling Discrete Flow Matching

May 9, 2026cs.LG

Discrete Flow Matching: Convergence Guarantees Under Minimal Assumptions

Flow Matching has recently emerged as a popular class of generative models for simulating a target distribution

μ_1

from samples drawn from a source distribution

μ_0

. This framework relies on a fixed coupling between

μ_0

and

μ_1

, and on a deterministic or stochastic bridge to define an interpolating process between the two distributions. The time marginals of this process can then be approximately sampled by estimating the transition rates, or more generally the generator, of its Markovian projection. This framework has recently been extended to the case of discrete source and target distributions, under the name Discrete Flow Matching (DFM). However, theoretical guarantees for such models remain scarce. In this paper, we study two DFM models on

\mathbb{Z}_m^d = \{0,\ldots,m-1\}^d

, sampled through time discretization, and derive non-asymptotic associated bounds for both of them. In contrast to previous work, we establish non-asymptotic bounds in Kullback--Leibler divergence for the early-stopped version of the target distribution. We also derive explicit convergence guarantees in total variation distance with respect to the true target distribution. Importantly, these bounds rely only on an approximation error assumption, relaxing standard score assumptions used in earlier works, while also yielding improved dependence on the vocabulary size

m

and the dimension

d

.

Le-Tuyet-Nhi Pham, Giovanni Conforti, Zhenjie Ren +1

École Polytechnique, CMAP, IP Paris Route de Saclay, 91120 Palaiseau, France · Università degli Studi di Padova, Via Trieste, 63, 35131 Padova, Italia · LaMME, Université Évry Paris-Saclay Boulevard François Mitterrand 91000, France

Flow Matching Generative Modeling Flow-Based Generative Modeling Discrete Flow Matching

May 8, 2026cs.LG

Trajectory as the Teacher: Few-Step Discrete Flow Matching via Energy-Navigated Distillation

Discrete flow matching generates text by iteratively transforming noise tokens into coherent language, but may require hundreds of forward passes. Distillation uses the multi-step trajectory to train a student to reproduce the process in a few steps. When the student underperforms, the usual explanation is insufficient capacity. We argue the opposite: the trajectory is the bottleneck, not the student. Each training trajectory is built through a chain of blind stochastic jumps with no evaluation of sequence quality; a single bad decision at an early midpoint propagates through subsequent steps, yet the student must imitate the result. Trajectory-Shaped Discrete Flow Matching (TS-DFM) replaces these blind jumps with guided navigation: a lightweight energy compass evaluates candidate continuations at each midpoint, selecting the most coherent. All shaping is training-only; inference cost is unchanged. On 170M-parameter language modeling, the shaped student at 8 steps achieves 32% lower perplexity than the 1,024-step teacher while being 128x faster, with gains consistent across source distributions and three evaluators of increasing scale. TS-DFM achieves the best perplexity of any discrete-generation baseline we compare against, including methods trained on 6x more data or using 5x larger models.

Amin Karimi Monsefi, Dominic Culver, Nikhil Bhendawade +3

1The Ohio State University · 2Apple

Flow Matching Diffusion Language Model Inference Language Model Distillation Flow-Based Generative Modeling Teacher-Student Learning Discrete Flow Matching

May 8, 2026cs.LG

Scaling Categorical Flow Maps

Continuous diffusion and flow matching models could represent a powerful alternative to autoregressive approaches for language modelling (LM), as they unlock a host of advantages currently reserved for continuous modalities, including accelerated sampling and tilting. Recently, several works have demonstrated the possibility of generating discrete data continuously by a simple flow matching process between a Gaussian and the one-hot encoded data distribution. They have further shown the feasibility of accelerated sampling via Categorical Flow Maps (CFMs), resulting in competitive sample quality in the few-step regime. However, this method had only been evaluated at relatively modest scales (

<1

B), leaving the question of its scalability completely open. In this article, we train a

1.7

B-parameter base flow model on

2.1

T tokens and self-distill it into a CFM that generates diverse, high-quality text in as few as

4

inference steps while maintaining near-data-level token entropy. Furthermore, we introduce a likelihood bound for CFMs in the semi-discrete setting, and show that they can be used to score the model on standard LM benchmarks, achieving results in the same range as discrete diffusion methods. Finally, we uncover some of the challenges that arise from training these models at scale, and we provide prescriptive insights on loss weighting and time scheduling.

Oscar Davis, Anastasiia Filippova, Pierre Ablin +4

Apple · University of Oxford

Language Model Scaling Flow Map Learning Flow-Based Generative Modeling Continuous Diffusion Language Models Text Generation Discrete Flow Matching

May 5, 2026q-bio.QM

Tree-Conditioned Edit Flows for Ancestral Sequence Reconstruction

Ancestral sequence reconstruction (ASR) aims to infer extinct protein sequences at internal nodes of a phylogenetic tree. Classical ASR methods are typically based on continuous-time Markov substitution models, but they treat sites largely independently and handle insertions and deletions only weakly or not at all. We introduce a tree-conditioned edit-flow model for variable-length ASR. Given two descendant sequences and their branch distances to a shared ancestor, the model reconstructs the ancestor through paired bidirectional edit trajectories constrained to agree on a common ancestral state. On a benchmark of experimentally evolved sequences with only context-independent substitutions, the model does not match the accuracy of the best classical method, yet still achieves reasonable performance despite being trained on natural sequences that include insertions, deletions, and substitutions. On a benchmark of natural homologous sequences with abundant insertions and deletions, the model most accurately localizes inferred evolutionary change.

Emil Sharafutdinov, Ingemar André

Center for Molecular Protein Science Lund University Box 124, 221 00 Lund

Flow Matching Phylogenetic Inference Sequence Modeling Discrete Flow Matching

May 1, 2026cs.LG

Binomial flows: Denoising and flow matching for discrete ordinal data

Flow-based generative modeling in continuous spaces exploit Tweedie's formula to express the denoiser (learned in training) as a score function (used in sampling). In contrast, this relation has been largely missing in the discrete setting where common approaches focus on learning discrete scores and rates. In this work we close this gap for discrete non-negative ordinal data by introducing Binomial flows. Our framework provides a simple recipe for training a discrete diffusion model which simultaneously denoises, samples, and estimates exact likelihoods. We verify our methodology on synthetic examples and obtain competitive results on real-world data sets.

Yair Shenfeld, Ricardo Baptista, Stefano Peluchetti

Flow Matching Flow-Based Generative Modeling Diffusion Models Discrete Flow Matching