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NeurIPS 2026

Verifiable Environments Are LEGO Bricks: Recursive Composition for Reasoning Generalization

Hao Xiang, Qiaoyu Tang, Le Yu, Yaojie Lu, Xianpei Han, Ben He, Le Sun, Bowen Yu, Peng Wang, Hongyu Lin, Dayiheng Liu

Reinforcement Learning (RL) with verifiable environments has emerged as a powerful approach for enhancing the reasoning capabilities of Large Language Models (LLMs). While prior research indicates that scaling environment quantity improves RL performance, existing manual or individual construction methods suffer from linear scaling limits, thereby hindering scalable reasoning generalization. This paper introduces RACES (\textbf{R}ecursive \textbf{A}utomated \textbf{C}omposition for \textbf{E}nvironment \textbf{S}caling), a framework that treats verifiable environments as composable building blocks that can be recursively assembled. The key insight is that when the codomain (output type) of one environment matches the domain (input type) of another, they can be automatically fused into a new verifiable environment, enabling recursive composition. RACES is instantiated with 300 individual environments and defines a set of composition operators (Sequential, Parallel, Sort, and Select) that induce diverse reasoning patterns. Extensive experiments show that RL training on these composite environments consistently enhances reasoning generalization. Specifically, RACES improves DeepSeek-R1-Distill-Qwen-14B by an average of 3.1 points (from 48.2 to 51.3) and boosts Qwen3-14B performance from 58.8 to 61.1 on five benchmarks, which are unseen during the construction of training environments. Moreover, RACES achieves performance comparable to training on 300 individual environments using only 50 base environments, demonstrating significant efficiency in environment utilization.

NeurIPS 2026

VeriWorld: A Verifiable Visual SWE-Bench for Spatial Reasoning in 3D Environments

Yan Zheng, Anthony Peng, XUYAO LIANG, Xiaoyan Cong, Nuo Chen, Bangya Liu, Zihan Wang, Wenyan Cong, Zhiwen Fan, Zhangyang &quot, Atlas&quot, Wang

Vision-language models (VLMs) are increasingly used for spatial tasks such as navigation and manipulation, where they must infer geometry and object relationships from visual input in order to act correctly. Existing benchmarks usually test perception and reasoning in isolation, making it hard to tell whether failures come from visual understanding, downstream reasoning, or the bridge between them. How can we evaluate whether a model can recover the right spatial structure from visual input and use it to make correct decisions? We introduce VeriWorld, a benchmark for spatial reasoning in interactive 3D environments with executable actions and deterministic verification. Each task is evaluated under three matched input settings -- visual-only, structured, and combined -- while the environment and objective remain fixed. This design isolates whether failures arise from perception, reasoning, or their interaction. VeriWorld brings together interactive 3D environments, code-based actions, deterministic verification, parameterized task generation, and controlled diagnostic evaluation in a single framework. Using this setup, we uncover two findings. First, models often succeed when given structured spatial information but fail when the same information must be inferred from visual input, revealing a recurring visual-to-structure gap. Second, action-space and harness design can change outcomes even under the same task and information condition, showing that interaction protocol is itself a confounding variable in spatial evaluation. VeriWorld is open-sourced to support reproducible and fine-grained evaluation of spatial reasoning in VLMs.

NeurIPS 2026

VeriVul: A Verification-Guided Framework for Generating Realistic Vulnerability Benchmarks

Ahmed Lekssays, Hamza Mouhcine, Issa Khalil

Evaluating machine-learning-based vulnerability detectors requires datasets that pair accurate labels with realistic code. Existing benchmarks satisfy at most one. Real-world collections rely on noisy commit-based labels because manual curation by security experts does not scale, while verified synthetic collections generate code from scratch that is too simple to resemble production software. The rapid advance of code LLMs adds a third pressure, since their training corpora absorb public CVE data and most widely cited vulnerability benchmarks, leaving static evaluations of such models prone to measuring memorisation rather than analysis. As model knowledge cutoffs continue to move forward, any fixed dataset risks becoming part of the next generation's training set. We present VeriVul, a framework that produces formally verified vulnerability data on demand. Given a CVE-fixing commit, it applies a vulnerability-aware backward program slicer to isolate the fragment relevant to the vulnerability, prompts a code LLM to expand the fragment into a self-contained program, and certifies the resulting program with the ESBMC bounded model checker, recording the verified label together with the trace that triggers the violation. Each verified program is paired with an ESBMC-verified counterpart that flips the label. We characterise the synthesised programs along vulnerability-relevant structural dimensions (e.g., control-flow density, pointer and array operations, struct-field access, and identifier diversity) and show that VeriVul dataset samples lie distributionally closer to real-world vulnerable code than the prior verified synthetic baseline, while remaining sufficiently complex to challenge state-of-the-art LLM-based detectors. In a prompted evaluation, Claude Opus 4.7 reaches only 52.6 percent accuracy on VeriVul dataset despite being given the full self-contained program. Because each sample carries the ESBMC counterexample and the violating statement, VeriVul also supports evaluation beyond binary classification, including root-cause identification and trace-grounded explanation. We release the framework, the slicer, the verification harness, and the generated dataset to support contamination-resilient evaluation of code LLMs as vulnerability analysts.

NeurIPS 2026

VeriTrip: A Verifiable Benchmark for Travel Planning Agents over Unstructured Web Corpora

Yuting Xu, Jiayi Tian, Jian Liang, Xin Xiong, Hang Zhang, Mu Xu, Xiao-Yu Zhang

Existing benchmarks have laid the foundation for travel planning agents by establishing API-centric paradigms. However, as the capabilities of Autonomous Agents continue to advance, their evaluation must evolve beyond simple tool execution toward handling the inherent complexities of the open web. Current benchmarks bypass core cognitive hurdles: they fail to account for information noise, ignore multi-source factual contradictions, and overlook the necessity of grounding visual perception into logical planning. We introduce VeriTrip, a verifiable benchmark designed to meet the increasing demands for agent robustness and reliability. VeriTrip shifts the evaluation focus to evidence-grounded reasoning over unstructured multimodal web corpora. It establishes a Multimodal Retrieval Base (MRB) derived from real-world sources, forcing agents to autonomously orchestrate queries across heterogeneous data. A synchronized Verifiable Knowledge Base (VKB) enables a cell-wise verification protocol that precisely quantifies factual reliability, distinguishing systematic reasoning failures from parametric hallucinations. Our evaluations across leading MLLMs reveal a critical \textit{retrieval-reasoning trade-off}: the cognitive load of autonomous retrieval significantly erodes instruction retention. VeriTrip provides the rigorous foundation necessary for the next generation of planning agents capable of operating in unconstrained, multimodal environments.

NeurIPS 2026

VeriScope: Measuring Verification-Ready Verilog Artifacts

Wei Zhang, Jian Yang, Jiajun Wu, Junhang Cheng, Chufan He, Yihang Lou, Xianglong Liu

Large language models (LLMs) are increasingly used in hardware-oriented coding workflows, yet open resources for evaluating first-pass RTL beyond execution remain limited. We present VeriScope, an open benchmark and evaluation suite of 568 problems spanning basic combinational gates through module-level designs and a 95-task L4+ top-end slice (92 L4 system tasks plus 3 L5 stress tests). A developer agent receives a natural-language task brief, returns a single RTL draft, and that artifact is evaluated through objective execution plus RTL-level and artifact-level review incorporating waveform and circuit evidence. Across 26 public models plus two 32B calibration baselines, the best systems reach about 84/100 combined score on the full benchmark but drop to the high 70s on L3–L4+. The 60/40 combined leaderboard largely tracks functional execution (Spearman 0.998 with a functional-only ranking), while artifact scores are most useful as a post-simulation screening signal: 29.6% of L3–L4+ simulation-passing submissions receive artifact score below 6 and therefore need additional verification evidence. A 100-sample manual taxonomy of such disagreements finds 70% testbench coverage gaps, 12% real RTL defects, and 18% judge hallucinations (Wilson 95% intervals reported in the analysis), showing that artifact review surfaces both under-tested passes and model defects, but should not be treated as a standalone leaderboard refinement.

NeurIPS 2026

VeriContest: A Competitive-Programming Benchmark for Verifiable Code Generation

Zichen Xie, Mrigank Pawagi, Yuxin Liu, Aaditi Rai, Lize Shao, John Berberian, Sicong Che, Wenxi Wang

Large language models can now generate useful code from natural language, but their outputs still come without correctness guarantees. Verifiable code generation offers a path beyond testing by requiring models to produce not only executable code, but also formal specifications and machine-checkable proofs. Progress in this direction, however, is difficult to measure: existing benchmarks are often small, focus on only one part of the pipeline, lack ground-truth proofs or rigorous specification validation, or target verification settings far from mainstream software development. We present VeriContest, a benchmark of 946 competitive-programming problems from LeetCode and Codeforces for verifiable code generation in Rust with Verus. Each problem pairs a natural language description with expert-validated formal specifications, judge-accepted Rust code, Verus-checked proofs, and positive and negative test suites. VeriContest is constructed through a three-phase pipeline that scales from manually verified seed problems to semi-automated expansion with human-in-the-loop review. To further strengthen benchmark quality, we use testing as an additional quality-assurance layer for validating postcondition completeness. VeriContest supports both isolated and compositional evaluation of specification generation, code generation, proof generation, and end-to-end verified program synthesis. Evaluating ten state-of-the-art models reveals a sharp gap between ordinary coding ability and verifiable code generation: the strongest model reaches 92.18% on natural-language-to-code generation, but only 48.31% on specification generation, 13.95% on proof generation, and 5.29% end-to-end. These results identify proof and specification generation as the central bottlenecks for current models and establish VeriContest as a rigorous platform for measuring and training future systems that generate code with machine-checkable correctness.

NeurIPS 2026

Veri-Sure: Multi-Agent RTL Code Generation with Temporal Tracing, Slicing and Formal Verification

Jiale Liu, Taiyu Zhou, Tianqi Jiang

In the rapidly evolving field of Electronic Design Automation (EDA), the deployment of Large Language Models (LLMs) for Register-Transfer Level (RTL) design has emerged as a promising direction. However, silicon-grade correctness remains bottlenecked by (i) limited test coverage and reliability of simulation-centric evaluation, (ii) regressions and repair hallucinations introduced by iterative debugging, and (iii) semantic drift as intent is reinterpreted across agent handoffs. In this work, we propose Veri-Sure, a multi-agent framework that establishes a design contract to align agents' intent and uses a patching mechanism guided by static dependency slicing to perform precise, localized repairs. By integrating a multi-branch verification pipeline that combines trace-driven temporal analysis with formal verification consisting of assertion-based checking and Boolean equivalence proofs, Veri-Sure helps improve functional correctness by enriching the simulation-driven debugging loop with localized diagnostic hints. We also introduce VerilogEval-v2-EXT, extending the original benchmark with 53 more industrial-grade design tasks and stratified difficulty levels, and show that Veri-Sure achieves state-of-the-art verified-correct RTL code generation performance, surpassing standalone LLMs and prior agentic systems. Code and dataset are available at https://anonymous.4open.science/r/Veri-Sure-D861.

NeurIPS 2026

Vendi Anomaly Scores for Efficient and Accurate Anomaly Detection

Amey Pasarkar, Adji Bousso Dieng

Anomaly detection (AD) is a critical task in machine learning and scientific discovery. Existing methods that operate on learned embeddings typically define anomalies through local density, isolation heuristics, or distance from a fitted distribution, making them sensitive to neighborhood scale, partitioning choices, or restrictive distributional assumptions. In this work, we introduce a new paradigm by formulating anomaly detection in terms of dataset diversity. We propose the Vendi Anomaly Score (VAS), which detects anomalies by quantifying how much a sample changes the diversity of the dataset, as measured by the Vendi Score, when removed. VAS captures both local redundancy and global data structure without relying on density estimation or partitioning heuristics. Moreover, VAS requires no hyperparameter tuning, instead adapting automatically to the spectral structure of the data. VAS is non-parametric and scales linearly with dataset size. Across 148 benchmark embedding datasets derived from 10 source datasets and 4 embedding architectures, VAS achieves state-of-the-art AD performance. We further validate VAS on large-scale ImageNet experiments, where it remains robust as both contamination rate and dataset scale increase.

NeurIPS 2026

Velocity Ambiguity Profiles: Time-Resolved Bayes-Risk Diagnostics for Flow Matching

Yunpeng Mei, Xiaowen Zhu, Chenyu Wang, Chenbo Xin, Hongjie Cao, Jiamin Wang, Jie Chen, Gang Wang

Flow matching trains a continuum of velocity regression problems but usually reports a loss averaged over interpolation time, obscuring which regions are limited by intrinsic ambiguity and which remain data-limited. We introduce the Velocity Ambiguity Profile (VAP), $\mathcal{A}_v(t)$, the time-local Bayes-risk floor of velocity prediction, and decompose time-resolved loss as $L_N(t)=\mathcal{A}_v(t)+R(t;N)$, where only the excess term $R(t;N)$ is reducible by more data or a different estimator. We prove two statistical benchmarks. In an intrinsic local-regression benchmark, $\mathcal{A}_v(t)$ enters the time-dependent noise factor of the standard nonparametric rate. In separated isotropic Gaussian mixtures, the Bayes velocity becomes locally affine, and a label-oracle residual-regression benchmark has parametric excess-risk scale $K\mathcal{A}_v(t)/N$, matched within the same separated residual Gaussian-location subproblem. Controlled Gaussian-mixture experiments validate this diagnostic through a dense transition sweep, calibrated oracle-to-blind and empirical-proxy audits, and a local controlled time-sampler stress test in which a frozen reducible-error proxy reduces reducible loss while cross-cell sensitivity delimits aggressive sampling. VAP turns an averaged flow-matching objective into a time-resolved diagnostic for locating ambiguity-limited and data-limited regions.

NeurIPS 2026

VecDBLens: A Modular Framework for Diagnosing Vector Databases Retrieval Pipelines

Yutong Zhou, Guoxin Kang, Wenxin Zhou, Haoyu He, Yuedong Zhu, Lei Wang, Wanling Gao, Fanda Fan, Jianfeng Zhan

Vector databases are increasingly deployed as retrieval pipelines in which representation, indexing, and query-time execution jointly determine accuracy, throughput, and cost. Existing vector database evaluations primarily focus on indexing while treating embeddings as fixed inputs and ignoring the role of query-time execution, making it difficult to decide whether a bottleneck should be addressed by changing the embedding model, the index, or the query-processing stages. To address the above limitation, we introduce \textbf{VecDBLens}, a modular attribution framework that treats the component under diagnosis as an \emph{evaluated object} and all remaining dataset, workload, parameter, and runtime factors as matched \emph{evaluation conditions}. VecDBLens reports stratified marginal effects, paired matched-condition differences, Flat-relative retention, and monotonicity audits, thereby turning vector database benchmarking from leaderboard ranking into a reproducible diagnostic procedure. VecDBLens reveals two key insights. First, retrieval performance is fundamentally upper-bounded by embedding quality, revealing that many apparent indexing failures are therefore representation-side limitations. Second, stronger index parameterization is not always beneficial: overly aggressive configurations can reshape neighborhood topology and cause recall regression. These results challenge the common practice of evaluating vector databases primarily through indexing and show that real-world limitations emerge from stage-wise constraints rather than any single module alone. VecDBLens provides a principled basis for identifying the true performance drivers of vector databases and for guiding their design in practical applications. The code is available at \url{https://anonymous.4open.science/r/VecDBLens-83A4}.

NeurIPS 2026

Variational Wasserstein Model on Riemannian Manifolds for Image Segmentation

Jisui Huang, Yue Wu, Ke Chen, Na Lei

The data fidelity term plays a crucial role in variational image segmentation. Recently, optimal transport (OT)-based variational models have improved segmentation by globally matching predicted feature distributions with reference distributions. However, existing OT-based methods usually rely on color or intensity similarity, which can be insufficient when foreground and background regions share similar appearance. We address this limitation by incorporating geodesic distance into the OT cost on a Riemannian feature manifold, allowing the transport cost to jointly encode spatial proximity, appearance similarity, and boundary information. The proposed model is well-defined: we prove existence of minimizers and convexity of the energy functional. It is also tractable: the OT terms admit differentiable transport-map representations, avoiding storage of the full pairwise transport matrix and enabling efficient gradient-based optimization. Experiments on BraTS and RESECT show that our method consistently outperforms traditional variational models, OT-based baselines, and prompt-based deep segmentation models, particularly when foreground and background have overlapping intensity or color patterns.

NeurIPS 2026

Variational Trajectory Optimization of Anisotropic Diffusion Schedules

Pengxi Liu, Zeyu Michael Li, Xiang Cheng

We introduce a variational framework for diffusion models with anisotropic noise schedules with a matrix-valued path $M_t(\theta)$ that allocates noise across subspaces. Central to our framework is a trajectory-level objective that jointly trains the score network and learns $M_t(\theta)$, which encompasses general parameterization classes of matrix-valued noise schedules. We further derive an estimator for $\partial_\theta \nabla \log p_t$ that enables efficient optimization of the $M_t(\theta)$ schedule. For inference, we develop an efficiently-implementable reverse-ODE solver that is an anisotropic generalization of the second-order Heun discretization algorithm. Across CIFAR-10, AFHQv2, FFHQ, and ImageNet-64, our method consistently improves upon the baseline EDM model in all NFE regimes.

NeurIPS 2026

Variational Inference via Entropic Transport Descent

Vincent Pacelli, Akash Ratheesh Babu, Evangelos Theodorou

Particle-based variational inference (ParVI) methods approximate an intractable target distribution by evolving an ensemble of interacting samples. Existing approaches rely predominantly on kernel-based repulsion (e.g., SVGD), which suffers from variance collapse in high dimensions and mode collapse on multimodal targets—pathologies caused by the absence of global transport structure. We introduce entropic transport descent (ETD), a ParVI family that frames each particle update as an entropy-regularized optimal transport problem. Derived from the JKO proximal scheme by lifting to the space of couplings and relaxing via the KL chain rule, each ETD iteration reduces to a Sinkhorn computation. The resulting transport plan provides global coordination, guiding each particle to nearby high-density proposals and naturally preserving multimodal structure. ETD can operate entirely score-free, requiring only pointwise evaluations of the unnormalized target density. Experiments on variance-collapse diagnostics, Bayesian logistic regression, neural networks, and molecular Boltzmann distributions show that ETD matches or outperforms SVGD, AGF-SVGD, and SGLD, with the largest gains in high-dimensional and multimodal settings.

NeurIPS 2026

Variational Cover Modification Steganography

Martin Benes, Rainer Böhme

Current approaches to learning-based image steganography are, at best, imperceptible, but their security is vulnerable to state-of-the-art detector networks. Variational cover modification steganography tackles this problem by training a generator network that can predict the parameters of the distribution of the least detectable stego-noise for a given cover image. It uses syndrome coding to embed the message within the distribution constraint and retrieve it exactly when a secret key is provided. Adversarial learning ensures that the generator evolves against a continuously refined detector. Experiments demonstrate significant security improvements, and several ablations support the generator architecture and the training protocol.

NeurIPS 2026

Variational Consequence-Driven Offline Reinforcement Learning

Wen Jiang, Ke Jiang, Jin Wang, Xiaoyang Tan

Offline reinforcement learning (RL) typically mitigates distribution shift by imposing divergence constraints on the action distributions of the learned and behavior policies. However, this paradigm cannot ensure the underlying dynamic consistency structure: even minor action deviations can lead to drastically different transitions, inadvertently driving the agent away from the offline dataset. To address this, we explore policy constraints through their induced state-consequence distributions rather than relying on pure action-distribution matching. Nevertheless, directly enforcing such consequence-aware constraints is computationally intractable without access to the true underlying dynamics model. To bypass this issue, we propose Structural Behavior Regularization (StBR), which replaces the intractable objective with a closed-form latent divergence. Structuring this latent space to reflect transition dynamics renders the latent divergence a theoretically bounded surrogate for the true consequence-distribution divergence. By regularizing the learned policy with this latent divergence, StBR adaptively tightens the behavior constraint in dynamics-sensitive regions, effectively preventing deviations outside the offline dataset. Empirically, we demonstrate that StBR achieves superior performance across diverse offline RL benchmarks.

NeurIPS 2026

Variational Active Flow Matching for Discrete Online Black-Box Optimization

Yashvir Singh Grewal, Daniel M. Steinberg, Thang Bui, Cheng Soon Ong, Edwin Bonilla

Many scientific design problems require identifying rare high-fitness objects in vast discrete spaces using costly black-box feedback. Variational active-generation methods, including variational search distributions (VSD) and conditioning by adaptive sampling (CbAS), address this by learning a distribution over high-fitness designs via inference on a level-set posterior. However, these methods rely on generators with explicit likelihoods, most commonly autoregressive models, creating a mismatch with modern non-autoregressive approaches, such as discrete diffusion and flow-based models, which refine designs in parallel and better capture multi-modal structure but have implicit marginal likelihoods. We introduce \textit{Active Flow Matching} (AFM), a variational active-generation framework that removes this likelihood bottleneck by reformulating level-set KL objectives over the conditional endpoint distributions of discrete flow models. AFM yields forward-, reverse-, and symmetric-KL objectives without requiring density evaluation. We show that forward-KL AFM is target-consistent, recovering the level-set posterior without access to marginal likelihoods. Empirically, across protein and small-molecule design tasks, AFM outperforms strong baselines, including autoregressive VSD and CbAS, inference-time guidance, KL-regularised fine-tuning, and Top-$K$ retraining.

NeurIPS 2026

Variance-Averse n-Step Offline Reinforcement Learning for Sparse Long-Horizon Environments

Guhyeon Kang, Minhae Kwon

Generative actors are transforming offline reinforcement learning (RL) by enabling expressive policy classes that model complex action distributions. However, this expressiveness also exposes a key challenge in heterogeneous datasets: generative policies can reproduce unreliable action modes whose return distributions exhibit high variance, occasionally yielding high returns by chance but lacking consistency. Consequently, maximizing the expected Q-value alone is insufficient for identifying reliable actions. We propose VAN-Flow (Variance-Averse n-step Flow), a framework that promotes reliable actions in generative offline RL. VAN-Flow combines (i) a categorical distributional critic, (ii) a variance-averse expectation operator that smoothly reweights atom probabilities to favor actions with both high returns and low dispersion, and (iii) a flow-matching generative actor guided via rejection sampling. Unlike CVaR or mean--variance objectives, the operator redistributes probability mass over the categorical return distribution without hard truncation or auxiliary penalty terms. Across more than 40 tasks from D4RL and OGBench, VAN-Flow consistently outperforms strong baselines, with the largest gains in long-horizon and high-variance regimes where reliable action selection becomes critical.

NeurIPS 2026

Variance-Adaptive Optimal Algorithm for Reinforcement Learning with MNL Function Approximation

Wonyoung Kim, Garud Iyengar, assaf zeevi, Min-hwan Oh

Reinforcement learning with multinomial logistic (MNL) function approximation has become an important framework due to its flexibility and broad applicability. While existing studies have established regret guarantees under worst-case analysis, they do not capture how performance depends on the variability of the interaction between the learner and the environment. In this paper, we develop a new theoretical analysis for MNL-based Markov decision processes that yields explicit variance-adaptive regret bounds. Our algorithm is computationally efficient and achieves the instance-wise optimal rate of regret, narrowing the gap between upper and lower bounds. Our numerical experiments validate that our method learns optimal policies more efficiently than conventional approaches.

NeurIPS 2026

Variance Reduction for Expectations with Diffusion Teachers

Jesse Bettencourt, Xindi Wu, Matan Atzmon, James Lucas, Jonathan Lorraine

Pretrained diffusion models increasingly serve as frozen teachers feeding downstream pipelines such as text-to-3D, single-step distillation, and data attribution. The teacher gradients these pipelines consume are Monte Carlo expectations over noise levels and Gaussian noise; their estimator variance dominates compute cost because each draw requires expensive upstream work, such as rendering, simulation, or encoding. We introduce CARV, a compute-aware variance-accounting framework that motivates a hierarchical Monte Carlo estimator: amortize the expensive upstream computation over cheap diffusion-noise resamples, sharpened by timestep importance sampling and a stratified inverse-CDF construction. Across diffusion-guided workloads, we obtain 2–3× effective compute multipliers, most from amortized reuse and approximately 25% additional gain from importance sampling plus stratification, without changing the objective. We also map regimes where these gains translate into improved downstream metrics versus regimes where they do not, such as DMD.

NeurIPS 2026

Variable-Length Generative Protein Design via Generalized Poisson Flow

Chaoran Cheng, Zhanghan Ni, Yanru Qu, Yuxin Chen, Ruihan Guo, Jiajun Fan, Ge Liu

The ability to generate variable-length proteins is crucial in protein design, where the optimal length is often unknown and tightly coupled to structural designability. Current state-of-the-art diffusion and flow-based generative models require the protein length to be predetermined before sampling, limiting their flexibility in exploring the feasible protein design space. To bridge this gap, we introduce Generalized Poisson Flow (GPFlow), a novel generative framework that enables variable-length generative modeling by learning the rate function that minimizes the negative log-likelihood of an inhomogeneous generalized Poisson process. We establish theoretical guarantees for recovering the joint multimodal distribution (both continuous and discrete) and for an upper bound on the KL divergence to the generated distribution. We evaluate GPFlow extensively across various protein design tasks, including unconditional structure and sequence generation and conditional motif scaffolding, to validate GPFlow’s effectiveness on both continuous and discrete modalities. Our results demonstrate GPFlow’s superior generative performance and quality, achieving the top designability and distributional fitness on unconditional generation, and ranking first on 10 out of 16 motif scaffolding tasks, with up to a 10-fold improvement in success rates on the most challenging targets.

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