Generative Flow Networks

Also known as GFlowNet

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8 papers in the last four weeks, with none the four weeks before. 0.1% of all new papers.

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Latest papers 40

Oct 6, 2026cs.LG

Learning a Mixture of GFlowNets

Learning an ensemble of GFlowNets to sample from a discrete target distribution has become a common approach for achieving better state space exploration and convergence than that of a monolithic sampler. However, these methods often add a substantial runtime overhead to the base model, and their conceptual connection remains elusive. To address this, we first propose a general-purpose theoretical framework for describing a mixture of GFlowNets, which we specialize into continuously (CI) and discretely indexed (DI) collections. On the one hand, we show CI GFlowNets can be interpreted through the lens of a random features expansion, provably boosting the sampler's expressivity in graph-structured tasks and reducing learning instability via spectral shifting. On the other hand, we demonstrate DI GFlowNets encompass prior approaches for GFlowNet training and provide the foundation for the newly proposed Stratum-Conditioned (SC) GFlowNets. This method, which is inspired by the Doob's h-transform of Markov chains, decomposes the state space according to a prescribed modular function and restricts each component to sample from a distinct subset of it. Importantly, SC GFlowNets support centralized and component-wise embarrassingly parallel training, and we show both of them significantly speed up learning convergence and mode coverage without introducing any non-negligible extra computation.

Tiago da Silva, Amauri H. Souza, Salem Lahlou

MBZUAI, UAE · Avra, Brazil & Federal Institute of Cear´a, Brazil

Generative Flow Networks

Oct 4, 2026cs.LG

Universality and Convergence of Generative Flows

Generative flows sample from an unnormalized target by training a flow to be balanced, and the training loss is the signal a practitioner watches. We ask what that signal is worth: whether a small loss certifies an accurate sampler, whether the loss can be driven to zero, and how fast gradient descent does so. The loss decides the first. Losses that compare the two sides of the balance by their difference bound, in total variation, the error of the sampler the flow implies, with explicit constants that do not involve the policy; flow-matching losses that compare them through a ratio admit no such bound, already on a single cycle, whenever their generator is continuous at balance. On graphs, the backward policy decides the other two. Once it is frozen, balance becomes invariance under the backward chain, so that existence is free on finite graphs, and one constant --- the norm of that chain's Green operator, which plays the role of an inverse spectral gap --- fixes the order of the curvature of the loss around the balanced flow, from above and below, and sets a floor under the rate at which training converges near it. The mechanism is that gradient descent diffuses the flow along the backward policy. For the squared-logarithm generator of detailed and trajectory balance, training the balance loss on states converges globally on every finite path-connected graph, from every positive initialization. The constant can be infinite while backward trajectories are short on average, and exact flow matching can then fail. The bounds and rates are tested by exact computation on enumerable state spaces, and every theorem carries a certification status computed from a Lean~4 development.

Leo Brunswic

LLM Suite Team, JP Morgan Chase & Co.

Flow Matching Generative Flow Networks Gradient Descent Dynamics

Sep 29, 2026cs.AI

Beyond Mode Collapse: Generating Diverse Synthetic Expert Conversations via Generative Flow Networks

High quality synthetic data is central to post training LLMs for adaptive AI applications that represent the diverse expert strategies and decisions in conversations. Prompting LLMs directly or conditioning them on end use scenarios yields low diversity data that collapses onto dominant modes. We propose a method to generate diverse high quality synthetic data using Generative Flow Networks (GFlowNets). We show that training GFlowNets to generate latent conversation structure using a Gaussian mixture density over key interaction features (e.g., confusion episode dynamics, scaffolding directive balance) enables sampling expert strategies in proportion to their prevalence in the training data. Across two structurally distinct domains, tutoring and emotional support dialogues, our GFlow based synthetic data generation approach offers a better balance of fidelity, mode coverage and authenticity than reinforcement-learning and end to end LLM baselines, without copying training data. Evaluated on three downstream outcome prediction tasks, classifiers trained on synthetic GFlowNet generated conversations provide a stronger training signal than competitive synthesis baselines.

Sumit Asthana, Michael Ion, Kevyn Collins Thompson

University of Michigan Ann Arbor, MI, USA

Generative Flow Networks Flow-Based Generative Modeling Synthetic Data Generation for Language Models Text Generation

Sep 29, 2026cs.CV

FlowMap-OPD: Rollout--Kernel Separation for On-Policy Distillation of Few-Step Flow-Map Generators

Few-step flow-map generators, including MeanFlow and consistency models, enable efficient sampling through long-range transport, yet their on-policy distillation remains underexplored. We introduce FlowMap-OPD, an on-policy distillation framework that separates student-state acquisition from teacher--student distribution comparison. A formulation based on state marginals establishes this separation, while flow--velocity consistency connects local supervision to the deployed long-range map. Within this framework, we develop flow-map, induced-velocity, and instantaneous-velocity distribution supervision, each paired with a separately specified native flow-map rollout. Cross-capacity ImageNet experiments across three teacher rewards identify instantaneous-velocity distribution supervision with independently tunable student consistency as the most effective choice. In text-to-image experiments, FlowMap-OPD demonstrates strong multi-specialist consolidation capabilities and surpasses multi-reward Flow-Map GRPO in task performance and convergence speed.

Zhiqi Li, Bo Zhu

Georgia Institute of Technology

Generative Flow Networks Flow Map Learning Consistency Distillation Flow-Based Generative Modeling On-Policy Distillation

Sep 28, 2026cs.LG

One Proposal for Every Margin: Zero-Shot Amortized Sequential Importance Sampling for Binary Matrices

In ecology, psychometrics, and the analysis of social and financial networks, binary matrices are often analyzed conditional on their observed row and column sums, which restricts the problem to a finite sample space of matrices with the same margins. Two fundamental problems are to count this space and to sample uniformly from it. Sequential importance sampling (SIS) addresses both with independent weighted samples and an unbiased count estimator, but its efficiency depends critically on the proposal distribution. Existing proposals are analytically designed, and their accuracy can vary substantially with the margins. We show that the ideal SIS proposal, under which every weight equals the count and the variance vanishes, is exactly the policy of a generative flow network (GFlowNet) with unit reward on every matrix that has the given margins. We therefore propose MarginFlow, a framework that turns the design of the proposal into a learning problem and amortizes it across margins by exploiting their self-similarity. Every partial matrix is itself an instance with reduced margins, so one set transformer that reads the remaining margins serves every margin. We train MarginFlow on a pool of 1904 margins and evaluate it zero-shot on 1190 held-out margins, synthetic and real, from

3\times3

to

870\times6

. On 1187 of the 1190 margins it matches or beats the best of 31 analytically designed configurations, chosen post hoc for each margin, and its median effective sample fraction is 99.8%. On the 56 margins where that best loses more than one nat of effective sample size, MarginFlow wins every one and raises the median effective sample fraction from 10.3% to 94.1%.

Ruishuo Chen, Weijia Li, Xun Wang +3

Institute for Interdisciplinary Information Sciences, Tsinghua University · Department of Statistics and Data Science, Tsinghua University

Importance Sampling Generative Flow Networks Flow-Based Generative Modeling

Sep 28, 2026cs.CV

CapField-OPD: Learning Continuous Capability Fields via Joint-Anchored Multi-Teacher On-Policy Distillation for Flow Models

Reward-specialized post-training produces strong experts for flow-based generative models, while multi-teacher on-policy distillation (OPD) consolidates their capabilities into a single student. Existing methods, however, route each prompt to a single teacher according to its semantic category, implicitly binding the desired capability to prompt content. This coupling makes capability invocation vulnerable to prompt perturbations and prevents users from explicitly adjusting the strength of the desired capability at inference time. In this work, we introduce CapField-OPD, an OPD framework that integrates multiple teachers into a continuous capability field through explicit capability coordinates. We use teacher models as anchors to construct this field, with the coordinates determining how their outputs are combined. Each capability configuration thus receives a unique supervision target, and capability control no longer depends on prompt semantics. Since the training anchors may not be optimal at inference time, we further profile the learned field on a small calibration set. The coordinate with the highest mean reward serves as the recommended default, while coordinates that are frequently optimal offer a promising candidate set for test-time scaling. Extensive experiments on compositional generation, text rendering, and visual aesthetics demonstrate that CapField-OPD consolidates multiple specialized teachers into a single student while preserving or surpassing their performance, reliably invokes the desired capabilities under semantics-preserving prompt variations, and supports continuous capability control and coordinate-based test-time scaling.

Pengyang Ling, Jiazi Bu, Yujie Zhou +6

University of Science and Technology of China · Shanghai Jiao Tong University · Fudan University +2

Generative Flow Networks Multi-Teacher Knowledge Distillation On-Policy Distillation Controllable Image Generation

Sep 27, 2026cs.AI

R $^2$ Flow: Recursive Self-Improvement via Recursive Skill Evolution

LLM-based agents can improve themselves across tasks by reusing and revising the skills they orchestrate into executable procedures. Flow-based training fits this loop: it samples procedures in proportion to reward, and the flow through each skill credits it for the next library revision. Three obstacles stand in the way of making this self-improvement reliable: flow training suffers strategy collapse over tree-structured histories; nonnegative flow-based credit rewards frequent use as if it were benefit; and library edits rest on the task reward the policy optimizes. We introduce R

^2

Flow, a recursive self-improvement framework that alternates policy learning, independent verification, and versioned skill-library updates on a shared-state orchestration graph. The graph merges histories that differ only in the order of independent steps, allowing flow training to pool evidence across equivalent executions. A flow-share readout of the trained flow, invariant to the backward policy, and a separate signed utility rank which skills to change, verifier evidence decides whether an edit is warranted, and a residual-variance plateau sets when to update. Committed edits reshape the graph the next policy learns on, realizing recursive skill evolution. Across question answering, mathematical reasoning, interactive decision making, and code generation, R

^2

Flow improves task accuracy and library-edit precision over heuristic orchestration, reinforcement learning, and skill-evolution baselines, and transfers across executors. Code is available at https://github.com/beita6969/r2flow.

Mingda Zhang, Qiang Huang, Yanjin Li +4

The Chinese University of Hong Kong, Shenzhen · Fudan University · University of Illinois at Urbana-Champaign +2

LLM Agent Self-Improvement Generative Flow Networks Agent Skill Learning

Sep 22, 2026cs.LG

WTF?! Simulation-Free Reinforcement Learning with Wasserstein-Tilted Flow Maps

Reward fine-tuning aims to update a pre-trained flow-based generative model to improve the downstream reward of its generated samples. Existing methods typically formulate this problem as sampling from a reward-tilted distribution, the solution to a KL-regularized reward-maximization problem. Here, we introduce an optimal transport regularizer built directly from the pre-trained drift. Unlike KL reward tilting, the resulting objective transports individual samples toward higher reward rather than reweighting the base distribution. We show that the resulting problem is equivalent to a deterministic optimal control problem on the flow. Given a pre-trained flow map, this equivalence yields a simulation-free reinforcement learning algorithm for fine-tuning generative flows. We call the resulting framework Wasserstein-Tilted Flow Maps (WTF), the first end-to-end fine-tuning recipe native to flow maps. The output is a fine-tuned flow map that retains strong reward-aligned performance at few-step inference budgets without post-hoc distillation. Experiments on ImageNet-256 and text-to-image show that WTF achieves higher reward with comparable or higher diversity than baselines, while requiring up to

280\times

less training compute. More broadly, we argue that accelerated samplers such as flow maps are essential infrastructure for efficient post-training, and that the dominant KL-regularized formulation is only one of many choices worth revisiting.

Abbas Mammadov, Jerry Y. Huang, Justin Lin +5

University of Oxford · Carnegie Mellon University

Reinforcement Learning Generative Flow Networks RL for Image Generation Flow-Based Generative Modeling RL for Generative Models RL Fine-Tuning+1

Sep 11, 2026cs.LG

Particle GFlowNets: Rethinking Generative Marginalization Models

Generative Marginalization Models (MaMs) have been recently introduced as efficient neural sampling models for any-order autoregressive modelling of discrete distributions. By learning both the marginal and conditional probabilities of a persistent-block Gibbs sampler, MaMs enable fast posterior evaluation with a single neural network forward pass. While prior work has considered MaMs to be distinct from Generative Flow Networks (GFlowNets), a well-established paradigm for inference in discrete stochastic models, we show that they are equivalent. Then, we also extend MaMs' sampling strategy to non-autoregressive generative processes. In particular, we describe an automatic criterion for full-state rejuvenation of the Gibbs sampler, derived from the Gelman-Rubin statistic, which plays a key role in speeding up learning convergence. Our experiments show that our method, called Particle GFlowNets, markedly accelerates training in large combinatorial spaces.

Tiago da Silva, Diego Mesquita, Salem Lahlou

MBZUAI · School of Applied Mathematics, Getulio Vargas Foundation

Markov Chain Monte Carlo Generative Flow Networks Generative Modeling Flow-Based Generative Modeling

Aug 6, 2026cs.LG

CrystalGRPO: Target-Aligned and Coverage-Preserving Reinforcement Learning for Flow-Based Crystal Structure Prediction

Flow-based generative models can efficiently produce candidate structures for crystal structure prediction (CSP), but their pretrained objectives do not directly optimize downstream target recovery. Reinforcement-learning post-training offers a flexible solution, yet existing approaches rely primarily on energy rewards and coordinate-only stochastic policies. Predicted energy does not identify the reference polymorph, while reward-driven concentration can reduce the candidate coverage required for Top-N recovery. We introduce CrystalGRPO, a CSP-aligned post-training framework that extends existing ODE-to-SDE policy constructions to the joint coordinate--lattice state. CrystalGRPO combines MACE-predicted energy with a StructureMatcher-based recovery score and provides two operating modes: CrystalGRPO-Q, which prioritizes single-draw recovery, and CrystalGRPO-C, which combines full-trajectory reference regularization with a coverage-aware group advantage to preserve finite-budget target recovery. Across MP-20 and MPTS-52 with PXRDGen and OMatG backbones, both variants reduce one- and twenty-sample RMSE relative to coordinate-only reinforcement in all four backbone--dataset settings. CrystalGRPO-Q consistently improves Top-1, whereas CrystalGRPO-C achieves a higher Top-20 across all settings.

Kaixiang Su, Hongfei Xue, Qiang Zhu

Department of Computer Science, University of North Carolina at Charlotte · Department of Mechanical Engineering and Engineering Science, University of North Carolina at Charlotte · North Carolina Battery Complexity, Autonomous Vehicle and Electrification (BATT CAVE) Research Center

Crystal Structure Prediction Group Relative Policy Optimization Generative Flow Networks RL Post-Training

Aug 5, 2026cs.LG

IFlowNets: Extending Generative Samplers to Learn Strategies in Incomplete Information Games

While many algorithms blend reinforcement learning (RL) with counterfactual regret (CFR) methods to leverage tradeoffs in computational speed and performance, there are fewer investigations into generative sampling frameworks in game theoretic applications in incomplete information games. We extend a generative flow network framework, Adversarial Flow Networks (AFlowNets), to incomplete information games, called Information Flow Networks (IFNs). We prove that previously established constraints for generative flow networks in complete information games are inadmissible for obtaining valid densities (corresponding to player strategies) and a valid training objective. We show that our proposed generalization, IFlowNets, alleviates this issue and strictly generalizes AFlowNets. In preliminary results for three standard game environments, IFlowNets perform comparably to or better than Outcome Sampling Monte Carlo Counterfactual Regret (OSMCCFR) and standard RL-based methods in performance and speed.

Conor M. Artman, Nicholas Di, Scott Perkins

AI Research Group, Lawrence Livermore National Laboratory · Deptartment of Statistics, Rice University · Strategic Competition Analysis Group, Lawrence Livermore National Laboratory

Imperfect-Information Games Generative Flow Networks

Aug 4, 2026stat.ML

Information-Geometric Forward Policy Training in GFlowNets

Generative Flow Networks (GFlowNets) have emerged as a flexible framework for amortised inference over discrete and mixed discrete-continuous objects, requiring only an unnormalised target density specified through a reward. In this work, we formulate forward-policy training in GFlowNets through the information geometry of the induced trajectory sampler. Treating the forward policy as an induced trajectory sampler, we show that its intrinsic first-order geometry is given by the Fisher-Rao metric of the trajectory family, and that the associated natural gradient provides the canonical local update whenever the corresponding Fisher information is computable or accurately approximable. We derive an exact decomposition of the trajectory Fisher into per-step conditional second moments, which clarifies when temporal score interactions vanish and when dense couplings remain under shared parameterisation. This leads to three computational regimes: settings with tractable exact Fisher information, settings where Monte Carlo estimators of the expected Fisher are sufficient, and structure-exploitable settings in which target locality or factorisation yields accurate approximations of the Fisher expectation. In the latter case, graphical-model tools such as exact marginalisation, separator methods, and belief propagation provide principled surrogates for natural-gradient updates. The resulting framework turns target structure into optimisation geometry and yields a tractable route to structure-aware forward-policy training in GFlowNets. We illustrate the framework empirically through examples comparing convergence and exploration behaviour under Riemannian and Euclidean optimisation.

Yordan Raykov, Rodrigo Veiga

School of Mathematical Sciences, University of Nottingham, Nottingham, UK

Information Geometry Natural Gradient Methods Generative Flow Networks

Aug 2, 2026cs.LG

AlphaG-OPD: Reliability-Gated Sibling Counterfactuals for On-Policy Distillation in Symbolic Alpha Factor Discovery

Symbolic alpha factor discovery can score a completed expression, but it provides no direct label for the structural decisions that produced it. Generative flow networks (GFlowNets) preserve a diverse, reward-proportional distribution over complete expressions, yet their trajectory-level objective does not compare unchosen sibling actions at an intermediate state. We introduce AlphaG-OPD, a structural on-policy distillation framework that turns terminal factor evaluations into local action guidance. Its design separates three decisions. Component I determines where to teach by exposing grammar-valid siblings at partial abstract-syntax-tree (AST) states visited by the current forward policy. Component II determines what is reliable enough to teach: it evaluates three supported siblings under four shared suffixes and admits a KL-bounded target only when their matched comparisons exhibit sufficient winner agreement and a positive empirical lower confidence bound (LCB). Component III determines how strongly and for how long to teach by consolidating accepted targets through bounded replay, score-indexed expiry, and forward-gradient balancing, without additional factor evaluations. Terminal reward, Trajectory Balance, the backward policy, grammar, and factor-pool rules remain unchanged. An equal-physical-score four-arm ablation tests paired teaching, reliability gating, and consolidation. Across China's CSI300, CSI500, and CSI1000 and the U.S. S&P 500, the complete method delivers strong cross-market performance over multiple random seeds.

Yaoyu Su

Quantitative Finance Generative Flow Networks On-Policy Distillation Counterfactual Learning Finance

Jul 15, 2026cs.CL

GFlowRL: Scaling Distribution-Matching RL to Large Language Models

Generative Flow Networks (GFlowNets) offer a promising alternative to reward-maximizing reinforcement learning (RL) for large reasoning models, encouraging diverse reasoning paths by matching reward distributions rather than collapsing to dominant modes. Recent work shows promise on math and code, but scaling GFlowNet-style RL to modern post-training pipelines remains difficult: as model size, rollout horizon, reward noise, and distributed-systems complexity grow together, a learned prompt-conditional partition function becomes a source of gradient instability and engineering overhead rather than a useful normalizer. Through systematic analysis, we find that the learned partition function, previously treated as essential, can be replaced by an in-batch Monte Carlo estimate computed from the rollout group already required for training. We propose GFlowRL, a streamlined GFlowNet-style RL algorithm that removes the auxiliary partition network entirely while preserving the reward-distribution-matching objective, completed by two stabilizers: importance-sampling correction for rollout/trainer drift and asymmetric flow-gap clipping for outlier residuals. GFlowRL exceeds all counterparts on math, code, and adversarial red-teaming benchmarks, reaching a Codeforces rating of 2048 at the 14B scale (within 25 Elo of o3-mini) and attaining the highest average ASR@1 on AdvBench and HarmBench, outperforming the previous SOTA multi-turn attacker in a regime where FlowRL, a prior GFlowNet-style method, diverges. The same recipe transfers to all evaluated MoE configurations up to 235B parameters, where FlowRL again fails to converge. To our knowledge, GFlowRL is the first GFlowNet-style RL algorithm to scale stably across both dense and sparse architectures. Code will be at: https://github.com/microsoft/gflowrl

Xiaodong Liu, Michael Xu, Jack W. Stokes +3

Microsoft Research

RL for Code Generation Reinforcement Learning RL for Language Model Reasoning Generative Flow Networks RL Post-Training

Jul 1, 2026cs.CL

Self-conditioned Flow Map Language Models via Fixed-point Flows

Self-conditioning is a core technique that enhances continuous flow-based language models, where the model learns to denoise generated text by conditioning on its own denoising estimate. While empirically successful, its performance improvements are poorly understood. Moreover, there is growing interest in the use of few-step generators based on flow maps, for which how to leverage self-conditioning is unclear. Here, we show that flow language models with self-conditioning perform a fixed-point iteration that improves generation through iterative refinement. We use this viewpoint to formulate fixed-point flows, a two-dimensional class of self-conditioned flows, where the first dimension represents the flow process and the second represents the fixed-point iteration. We show that fixed-point flows define valid flow maps, and show that they can be distilled from self-conditioned flow models by compressing both fixed-point iterations and the flow process, the former with fixed-point distillation and the latter with flow map distillation. Our resulting flow map language model, FMLM

^\star

, outperforms state-of-the-art self-conditioned models and few-step models in one- and few-step generation on OpenWebText. Code is available at https://github.com/Ugness/self-conditioned-fmlm.

Jaehoon Yoo, Wonjung Kim, Floor Eijkelboom +4

KAIST · University of Amsterdam · Carnegie Mellon University

Normalizing Flows One-Step Generative Modeling Generative Flow Networks Flow Map Learning Continuous Normalizing Flows Language Model Distillation+2

Jun 23, 2026cs.CL

Posterior Refinement: Fast Language Generation via Any-Order Flow Maps

Non-autoregressive generation offers a powerful paradigm for iterative refinement, allowing models to recursively critique, erase and regenerate arbitrary subsets of tokens. However, existing non-autoregressive models fail to realize this potential. Masked Diffusion Models (MDMs) suffer from factorization error, causing sample quality to collapse when generating multiple tokens simultaneously. Flow Map Language Models (FMLMs) circumvent this bottleneck via joint sequence transport for excellent few-step generation, but sacrifice the inference-time flexibility of MDMs. We introduce FMLM+, a framework that bridges this gap by equipping FMLM with masking-style noise schedules. While generating the full sequence in a single step, FMLM+ simultaneously scores the global consistency of each token a posteriori. We leverage this to introduce Posterior Refinement, a novel inference-time refinement strategy that enables the model to adaptively self-correct its outputs, matching the performance of discrete baselines with 32x fewer NFEs. Across diverse benchmarks, we demonstrate that FMLM+ with Posterior Refinement improves the speed--quality tradeoff over both MDM and FMLM families, providing a scalable foundation for high-fidelity language modeling.

Manan Agarwal, Sheel Shah, Chanhyuk Lee +6

Carnegie Mellon University · KAIST

Non-Autoregressive Text Generation Generative Flow Networks Flow-Based Generative Modeling Efficient Language Model Inference

Jun 23, 2026cs.LG

FlowPipe: LLM-Enhanced Conditional Generative Flow Networks for Data Preparation Pipeline Construction

Data preparation pipelines improve data quality in machine learning by transforming raw tables into learning-ready data through sequential cleaning and feature transformation operators. However, automatically constructing such pipelines is computationally difficult because operator sequences are combinatorial and end-to-end evaluation is expensive. Existing state-of-the-art (SOTA) Multi-DQN methods still face three key limitations: decoupled value estimators weaken long-horizon credit assignment, dataset context is only weakly injected into the policy, and exploration is inefficient in a sparse search space with many invalid states. To address these issues, we propose FlowPipe, a unified framework that formulates pipeline synthesis as conditional probabilistic flow generation over a directed acyclic graph. FlowPipe uses Conditional Generative Flow Networks (C-GFlowNets) with a Trajectory Balance objective to connect terminal validation rewards with early pipeline decisions. It further introduces Deep Semantic Modulation through Feature-wise Linear Modulation (FiLM), allowing LLM-derived logical priors to condition the policy's internal activations according to dataset semantics. In addition, FlowPipe incorporates failure awareness into the flow objective to avoid invalid states and concentrate search on high-potential regions. Experiments on two benchmark suites with 74 real-world datasets show that FlowPipe outperforms SOTA baselines, improving accuracy by 11.96% on average and achieving 12.5x faster training convergence. Source code is available at https://github.com/KunyuNi/FlowPipe.

Kunyu Ni, Lei Cao, Jie He +4

Ocean University of China China · University of Arizona USA · University of Science and Technology Beijing China +1

Generative Flow Networks Flow-Based Generative Modeling Conditional Generative Modeling

Jun 15, 2026cs.AI

Latent Thought Flow: Efficient Latent Reasoning in Large Language Models

Large Language Models (LLMs) increasingly rely on intermediate reasoning, yet explicit Chain-of-Thought (CoT) suffers from a linguistic space bottleneck: each thought must be decoded into tokens, causing high inference overhead. Latent reasoning moves deliberation into continuous space, but existing methods mostly learn deterministic or reward-maximizing paths, lacking a principled way to allocate probability across trajectories with different correctness and costs. We propose Latent Thought Flow (LTF), which models reasoning as variable-length continuous trajectories and trains a sampler to match a reward-induced posterior over answer quality and computation cost. We instantiate this with a continuous GFlowNet using stochastic latent transitions. To handle sparse answer supervision, we introduce an Entropy-Weighted Subtrajectory Balance objective for intermediate rewards and a reference-prior regularizer to anchor exploration. Experiments under finetuning and transfer learning settings show that LTF outperforms explicit CoT and latent reasoning baselines, improving accuracy by 9.5% while reducing reasoning length by 27.2% on average compared with strong latent reasoning baselines.

Xiandong Zou, Jing Huang, Jianshu Li +1

Singapore Management University · Ant Group

RL for Language Model Reasoning Efficient Language Model Reasoning Generative Flow Networks LLM Inference Acceleration Continuous Latent Reasoning Latent Reasoning

Jun 14, 2026cs.LG

Proximal Policy Optimization for Amortized Discrete Sampling

This paper explores policy gradient algorithms for training stochastic policies to sample from structured discrete probability distributions under the Generative Flow Network (GFlowNet) framework. Building on extensive theoretical connections between GFlowNets and entropy-regularized reinforcement learning, we derive equivalents of standard policy gradient algorithms for training GFlowNets, as well as experimentally explore their various methodological aspects, including baseline training and advantage estimation. Most importantly, our work is the first to derive and successfully apply proximal policy optimization to GFlowNets, showing its improved convergence speed and data efficiency compared to standard GFlowNet training objectives on benchmarks ranging from synthetic energies to molecular graph generation.

Anna Zykova-Myzina, Timofei Gritsaev, Daniil Tiapkin +1

HSE University · Constructor University · CMAP, CNRS, École polytechnique, IPP

Molecular Graph Generation Generative Flow Networks Policy Gradient Methods Proximal Policy Optimization

Jun 4, 2026cs.RO

Flow-based Policy Adaptation without Policy Updates

Leveraging prior knowledge from pretrained policies, foundation models, or human operators offers an efficient alternative to learning robot skills from scratch. However, these agents often provide actions that are suboptimal, noisy, or misaligned with task-specific expert behavior. We propose GLOVES, a family of flow-based adaptation methods that correct non-expert actions by transporting them toward an expert action distribution. Rather than replacing agentic control with full autonomy, GLOVES performs selective action-level adaptation, improving task success while preserving agent intent. The learned flow also provides a natural in-distribution scoring mechanism through reverse flow evaluation. We use this signal as an intervention gate: actions that appear consistent with the expert distribution are passed through unchanged, while anomalous or out-of-distribution (OOD) actions are corrected. In this way, assistance is only provided when necessary. GLOVES requires only limited expert supervision, using a small number of demonstrations or reusable successful skill segments. By learning local expert action patterns and stitching them during execution, GLOVES provides a lightweight shared-control module for robust action adaptation across tasks and environments. Code and demos are available at ripl.github.io/GLOVES_web.

Luzhe Sun, Jingtian Ji, Haoran Chen +2

Toyota Technological Institute at Chicago · Stony Brook University

Robot Policy Learning Robot Policy Adaptation Robot Skill Learning Generative Flow Networks Imitation Learning Shared Autonomy

Jun 4, 2026cs.LG

Your GFlowNet Secretly Learns an Optimal Transport Plan

Generative Flow Networks (GFlowNets) are a framework for sampling structured objects via stochastic trajectories in a directed graph. In this work, we establish a theoretical connection between non-acyclic GFlowNets and optimal transport (OT). We show that fixing the initial flow distribution in a minimum-flow GFlowNet reduces its objective to a Kantorovich OT problem with graph-induced shortest path costs. At the optimum, the learned GFlowNet policy therefore encodes an optimal transport plan from the source distribution to the target distribution: we show that sampling trajectories from the minimum-flow GFlowNet recovers the corresponding optimal coupling. Our formulation enables applying the GFlowNet learning framework to OT problems on large graphs via edge flows and neural parameterization. Experiments confirm agreement with exact OT solvers and demonstrate that GFlowNets can learn high-quality transport plans.

Ian Maksimov, Nikita Morozov, Denis Belomestny +1

1HSE University · 2Duisburg-Essen University

Generative Flow Networks Flow-Based Generative Modeling Optimal Transport

May 29, 2026cs.LG

Scalable Inference-Time Annealing with Surrogate Likelihood Estimators

A long standing challenge in computational chemistry and biophysics is efficiently sampling the Boltzmann distribution of molecules. Advances in generative modeling have been proposed to address the limitations of conventional sampling techniques by eliminating the computational cost of simulation. A promising direction is iteratively finetuning diffusion models along a temperature ladder whereby training data is generated via importance sampling during inference-time annealing. Unfortunately, these methods require computing a divergence over the score field to estimate importance weights, rendering them intractable for larger systems. Here we present scalable inference-time annealing (SITA), which retrains flow-based models to generate samples at progressively lower temperatures using an energy-based model to facilitate fast surrogate likelihoods. We demonstrate state-of-the-art performance on both Alanine Dipeptide and Alanine Tripeptide while avoiding costly divergence terms. Our code is available at https://github.com/countrsignal/sita.git

Daniel Peñaherrera, Rishal Aggarwal, David Ryan Koes

CMU-Pitt PhD Program in Computational Biology · Dept. of Computational & Systems Biology, University of Pittsburgh, Pittsburgh, PA 15260, USA

Generative Flow Networks

May 20, 2026cs.AI

Conflict-Aware Additive Guidance for Flow Models under Compositional Rewards

Inference-time guided sampling steers state-of-the-art diffusion and flow models without fine-tuning by interpreting the generation process as a controllable trajectory. This provides a simple and flexible way to inject external constraints (e.g., cost functions or pre-trained verifiers) for controlled generation. However, existing methods often fail when composing multiple constraints simultaneously, which leads to deviations from the true data manifold. In this work, we identify root causes of this off-manifold drift and find that the approximation error scales severely with gradient misalignment. Building on these findings, we propose Conflict-Aware Additive Guidance (

g^\text{car}

), a lightweight and learnable method, which actively rectifies off-manifold drift by dynamically detecting and resolving gradient conflicts. We validate

g^\text{car}

across diverse domains, ranging from synthetic datasets and image editing to generative decision-making for planning and control. Our results demonstrate that

g^\text{car}

effectively rectifies off-manifold drift, surpassing baselines in generation fidelity while using light compute. Code is available at https://github.com/yuxuehui/CAR-guidance.

Xuehui Yu, Fucheng Cai, Meiyi Wang +2

Smart Systems Institute, National University of Singapore, Singapore · Faculty of Computing, Harbin Institute of Technology, Harbin, China · School of Computing, National University of Singapore, Singapore

Constrained Generative Modeling Diffusion Model Guidance Generative Flow Networks Flow-Based Generative Modeling Inference-Time Guidance

May 19, 2026cs.CV

Distribution Matching Distillation without Fake Score Network

Distribution Matching Distillation (DMD) provides an effective distribution-level correction for few-step generation, while relying on an auxiliary fake-score network to track the evolving generative distribution. Recent work combines DMD-style objectives with flow-map generators to exploit both forward-divergence training and reverse-divergence correction. The fake-score estimator remains an additional component with memory and update overhead. In this work, we study whether this explicit tracker can be avoided when the generator itself has a flow-map structure. We propose Fake-Score-network-Free DMD (FSF-DMD), a DMD formulation for flow-map generators that replaces the auxiliary fake-score estimator with a generator-induced pseudo-velocity surrogate. The key observation is that the endpoint pseudo-velocity of a flow-map generator provides a tractable proxy for fake-velocity estimation, allowing the generator itself to supply the reverse-divergence signal. Building on this observation, we derive a practical objective, extend it with flow-map-consistent backward simulation, and introduce a self-teacher variant for training from scratch. In our ImageNet-1K

256 \times 256

experiments, FSF-DMD improves flow-map baselines, reaches lower FID than the listed DMD2 comparisons in the flow-map-initialized setting, and remains effective under flow-matching initialization and training from scratch.

Youngjoong Kim, Deokyeong Lee, Jaesik Park

Department of Computer Science and Engineering, Seoul National University · Department of Computer Science and Engineering, Sogang University Seoul, Republic of Korea

Diffusion Model Distillation Few-Step Diffusion Sampling Generative Flow Networks Flow-Based Generative Modeling Distribution Matching Distillation

May 16, 2026cs.CV

CAB: Accelerating Flow and Diffusion Sampling via Rectification and Corrected Adams-Bashforth

Flow and diffusion models achieve high-fidelity, high-resolution image synthesis, but often require many function evaluations (NFEs) at sampling time. Existing acceleration methods either require additional training through distillation or rely on training-free high-order solvers, and both can degrade sample quality at low NFE budgets. We propose CAB (Corrected Adams-Bashforth), a training-free sampler that accelerates both flow and diffusion models. CAB first transforms the sampling dynamics to a common rectified coordinate system, and then applies a multistep Adams-Bashforth predictor augmented with a simple correction term based on past velocity evaluations and therefore incurs no additional NFEs. The resulting method is simple, has the same algorithmic form across model classes, and has at least third-order local truncation error and second-order global error. Experiments on pretrained flow and diffusion models, including class-conditional and large-scale text-to-image benchmarks, show that CAB improves quality-NFE trade-offs in the low-step regime of 6-20 NFEs. It also remains competitive with strong training-free samplers at higher step counts across most tested models. The official implementation is available at https://github.com/Anuska-Roy/CAB.

Anuska Roy, Pravin Nair

Department of Electrical Engineering Indian Institute of Technology Madras, Chennai, India

Few-Step Diffusion Sampling Generative Flow Networks Diffusion-Based Image Generation Flow-Based Generative Modeling Diffusion Model Inference Acceleration

May 14, 2026cs.LG

$f$ -Trajectory Balance: A Loss Family for Tuning GFlowNets, Generative Models, and LLMs with Off- and On-Policy Data

In GFlowNets and variational inference, it has been shown that the mean square error between target and model log probabilities is an effective, low variance, surrogate loss for training generative models. This loss has the property that when evaluated \emph{on-policy} its gradients correspond to those of the KL divergence, while \emph{off-policy} it remains a valid loss with the same global minimizer. In this work, we demonstrate that this construction can be extended to the whole family of

f

-divergences, leading to a family of losses whose on-policy gradients are that of the corresponding

f

-divergence, but retain the same global minimizer off-policy. Specifically, we show that the on-policy gradients lead to a one to one correspondence between translation invariant loss functions on the target and model log probabilities, and

f

-divergences. This equivalence allows us to design new surrogate loss functions for tuning a wide class of generative models that inherit the properties of the corresponding

f

-divergence, such as being more mode covering, whilst being applicable to off-policy data. We apply our losses on a range of tasks, including classic synthetic examples, SynFlowNets for molecule discovery, and asynchronous large language model (LLM) tuning, demonstrating that our models retain their predicted properties on- and off-policy in a wide class of generative models.

Jake Fawkes, Jason Hartford

Department of Statistics, University College London, UK · Valence Labs, London, UK · Recursion, London, UK.

Generative Flow Networks Variational Inference

May 13, 2026cs.AI

SkillFlow: Flow-Driven Recursive Skill Evolution for Agentic Orchestration

In recent years, a variety of powerful LLM-based agentic systems have been applied to automate complex tasks through task orchestration. However, existing orchestration methods still face key challenges, including strategy collapse under reward maximization, high gradient variance with opaque credit assignment, and unguided skill evolution whose decisions are typically made by directly prompting an LLM to judge rather than derived from principled training signals. To address these challenges, we propose SkillFlow, a flow-based framework that takes a trainable Supervisor as the agent and a structured environment with dynamic skill library and frozen executor, automating task orchestration through multi-turn interaction. SkillFlow employs Tempered Trajectory Balance (TTB), a regression-based flow-matching loss that samples trajectories proportional to reward, preserving diverse orchestration strategies rather than collapsing to a single mode. The same flow objective yields a jointly learned backward policy that provides transparent per-step credit assignment at zero additional inference cost. Building on these flow diagnostics, a recursive skill evolution mechanism determines when to evolve, what skills to create or prune, and where decision gaps lie -- closing the loop from training signal to autonomous capability growth. Experimental results on 14 datasets show that SkillFlow significantly outperforms baselines across question answering, mathematical reasoning, code generation, and real-world interactive decision making tasks. Our code is available at https://anonymous.4open.science/r/SkillFlow-E850.

Mingda Zhang, Tiesunlong Shen, Haoran Luo +4

The Chinese University of Hong Kong, Shenzhen · National University of Singapore · Nanyang Technological University +1

LLM Agent Orchestration LLM Agent Self-Improvement LLM Agent Skill Learning Generative Flow Networks RL for LLM Agents

May 9, 2026cs.CV

Restoration-Aligned Generative Flow Models for Blind Motion Deblurring

Generative flow models offer powerful priors learned from large-scale natural images, but directly adapting them to restoration tasks such as motion deblurring causes severe fidelity degradation, as their training objective is inherently misaligned with restoration. We present DeblurFlow, a framework that resolves this misalignment by reformulating the flow trajectory itself: we replace the noise endpoint with the blur observation, which makes the underlying vector field coincide with the residual error between blur and clean images. Under this formulation, the standard flow matching loss naturally takes the form of a residual loss, allowing pretrained flow models to be optimized under restoration-aligned objectives via LoRA adaptation. This formulation further enables a dual-expert sampling strategy: a fidelity expert provides a high-fidelity initialization, e.g., PSNR 33.69 dB, and DeblurFlow enhances perceptual quality with only a marginal fidelity reduction to 33.05 dB, whereas directly applying a generative model on top of a fidelity expert decreases PSNR to 27.60 dB. To make this practical, we further introduce r-space, a latent space tailored for residual decoding rather than image reconstruction, which reduces encoder-decoder cost by up to 9

\times

over standard VAE latents. Extensive experiments on GoPro, HIDE, RealBlur, and RWBI demonstrate that DeblurFlow achieves strong restoration fidelity and perceptual realism, while remaining computationally practical.

Insoo Kim, Jinwoo Shin

1NAVER Cloud · 2KAIST AI

Flow Matching Image Deblurring Generative Flow Networks Image Restoration Flow-Based Generative Modeling

May 7, 2026cs.LG

Conservative Flows: A New Paradigm of Generative Models

Modern generative modeling is dominated by transport from a noise prior to data. We propose an alternative paradigm in which generation is performed by a discrete stochastic dynamics that leaves the data distribution invariant, initialized from data-supported states rather than from noise. The framework can utilize any pretrained flow model. We develop two probability-preserving sampling mechanisms, a corrected Langevin dynamics with a Metropolis adjustment and a predictor-corrector flow, that operate directly on existing checkpoints. We validate the framework on a synthetic Swiss-roll target, ImageNet-256 and Oxford Flowers-102, where our samplers consistently improve over the original generation procedures.

Eshed Gal, Md Shahriar Rahim Siddiqui, Moshe Eliasof +1

The University of British Columbia Vancouver, Canada · University of Cambridge Cambridge, United Kingdom

Langevin Dynamics Generative Flow Networks Generative Modeling Flow-Based Generative Modeling

May 3, 2026cs.LG

Stable GFlowNets with Probabilistic Guarantees

Generative Flow Networks (GFlowNets) learn to sample states proportional to an unnormalized reward. Despite their theoretical promise, practical training is often unstable, exhibiting severe loss spikes and mode collapse. To tackle this, we first assess the sensitivity of GFlowNet objectives, demonstrating that a small Total Variation (TV) distance between the learned and target distributions does not preclude unbounded training loss. Motivated by this mismatch, we establish converse guarantees by deriving loss-to-TV bounds that certify global fidelity from bounded trajectory balance losses. Lastly, we propose Stable GFlowNets, an algorithm that leverages our theoretical results to stabilize training, and empirically demonstrate improved training behavior and superior distributional fidelity.

Zengxiang Lei, Ananth Shreekumar, Jonathan Rosenthal +6

Lyles School of Civil and Construction Engineering, Purdue University, IN, USA · Department of Computer Science, Purdue University, IN, USA · Computer Science and Engineering, University of California, Santa Cruz, USA

Generative Flow Networks Flow-Based Generative Modeling