Constrained Generative Modeling

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20 papers in the last four weeks, up 300% on the four weeks before. 0.2% of all new papers.

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Latest papers 90

Oct 7, 2026cs.AI

Think Before You Paint: Recursive Latent Reasoning for Diffusion Models

Diffusion models generate realistic images but often fail on visual reasoning tasks, such as filling in a Sudoku or drawing the path through a maze. When a discrete symbolic representation is available, recursive methods such as the Tiny Recursive Model (TRM) solve even hard instances of these puzzles. We ask how such reasoning can be carried over to pixels, where no symbolic representation is available. We propose Painter-Thinker (PaTh): a small recursive network (the Thinker) reasons over a grid of learned tokens that encode the noisy image and the conditioning, refines a latent state within every denoising step, and steers a frozen diffusion model (the Painter) through ControlNet adapters. The Thinker is trained with the standard reconstruction loss alone, without symbolic targets, a solver, or a verifier. PaTh solves 92.5% of hard MNIST Sudoku puzzles (prior best 75%) and 71.2% of extreme ones (prior best 4.1%), with 10M parameters against 82M for a standard diffusion model. It also improves on mazes, Queens, and CLEVR scenes with specified spatial relations, and its advantage grows with problem size. Diagnostic experiments show that PaTh recovers from injected mistakes that the diffusion model cannot repair, especially when many cells are wrong. Together, these results show that reasoning mechanisms developed for symbolic data can be integrated into pixel-space diffusion without symbolic supervision, opening a path toward generating data under increasingly complex constraints.

Paweł Skierś, Małgorzata Grzanka, Wojciech Masarczyk +2

Warsaw University of Technology · IDEAS Research Institute · University of Amsterdam

Latent Visual Reasoning Diffusion Models Constrained Generative Modeling Pixel-Space Diffusion Models

Oct 7, 2026astro-ph.IM

Constrained Diffusion for Data-Scarce Orbital Monte Carlo in Constellation Tasking

Constellation Monte Carlo results depend on the orbital population used to evaluate a tasking policy. With scarce reference trajectories, replay limits geometric diversity, while independent orbital-element jitter can violate physical constraints. We study constrained diffusion for orbital-population augmentation. A force-conditioned diffusion model learns a 13-dimensional orbital prior, recovering semimajor axis from perigee altitude and eccentricity; Basilisk propagates each sample under one of five force-model tiers. Using 800 reference trajectories, we compare diffusion with jittered bootstrap, per-tier Gaussian mixtures, and a conditional variational autoencoder, and evaluate distributional fidelity, support shift, classical astrodynamics diagnostics, and 4,000 paired GoDSAT-compatible campaigns. The largest diffusion model achieves held-out trajectory MMD of 0.0171 +/- 0.0239, similar to bootstrap (0.0170) and the mixture (0.0198), but samples farther from training priors (median nearest-training distance 2.7 versus 0.10 standardized units). All generators fail to match the shifted-blind population (classifier AUC 0.991-0.998). Endpoint-conditioned samples satisfy Lambert boundaries but have greater interior error than the matched Lambert reference (29.2 versus 5.7 km mean RMSE). Residual diffusion improves selected sparse forecasts and catalog-mode recall but does not outperform classical estimators on custody ranking. In a fixed 16-satellite configuration, diffusion yields similar mean custody to replay and bootstrap, while the force-tier mixture shifts custody by about 5.5 percentage points. Constrained diffusion supports local, in-support augmentation but cannot replace orbital dynamics or serve as an operational posterior. Orbital-population construction is a consequential source of uncertainty in constellation analysis.

Omar Ramadan, Sam Siavoshian, Amir Kashif Saeed +3

Whiting School of Engineering Johns Hopkins University 3400 N. Charles St. Baltimore, MD 21218, USA

Constrained Generative Modeling Physics-Informed Diffusion Models LEO Satellite Networks

Oct 6, 2026cs.LG

Evolutionary One-Step Generators: Fast and Diverse Sampling for Discrete Design

Several discrete design tasks, such as molecular discovery, require diverse collections of useful candidates at low computational cost. High validity alone does not guarantee a useful candidate library: repeatedly generating the same valid structures leaves few distinct alternatives. Training for both feasibility and diversity is challenging because many relevant criteria can only be evaluated after hard decoding. To address this challenge, we propose EGO (Evolutionary Generators with One-step inference), a framework for training compact generators directly on discrete outputs. The method combines distribution matching with structural constraints and optional diversity or history-dependent rewards, using antithetic low-rank evolution strategies without requiring criterion-specific differentiable surrogates. Once trained, the generator produces the entire graph in a single neural-network evaluation. On molecular generation benchmarks, our compact generator achieves over

50\times

the valid-and-unique yield per estimated dense operation compared to recent one-step flow-map baselines while retaining high chemical validity. In scaffold completion, EGO achieves an observed

44.3\times

speedup over MoLeR in generation to SMILES and produces approximately

10\times

as many filter-passing proposals within matched time budgets for generation and screening. Beyond chemistry, EGO produces

1.54\times

as many distinct held-out elite architectures as relaxed gradient training on NAS-Bench-101. The low generation cost may enable real-time candidate generation across discrete design tasks, supporting interactive exploration of constrained design spaces and rapid construction of candidate sets for downstream evaluation.

Marcus Vukojevic, Erik Nielsen, Veronica Lachi +2

University of Trento, Italy · UiT The Arctic University of Norway, Tromsø, Norway

Constrained Generative Modeling Graph Generation Molecular Graph Generation One-Step Generative Modeling Molecular Generation

Oct 6, 2026cs.LG

OxiGen: Oxidation-State-Aware Crystal Generation

Generative models have the potential to accelerate inorganic materials discovery by enabling inverse design, but generating experimentally realisable crystals remains challenging. Oxidation states are widely used to assess the compositional validity of crystals and guide inorganic materials discovery. While existing generative models for crystals can generate materials with charge-neutral oxidation-state assignments, they poorly reproduce the distributions of oxidation states observed in synthesised materials. To address this limitation, we propose OxiGen, an oxidation-state-aware crystal diffusion model that explicitly represents oxidation states during generation. OxiGen enforces global charge neutrality by construction using a structured output layer with exact inference over a finite-state automaton. Empirically, OxiGen substantially improves oxidation-state fidelity, generates the highest rate of stable, unique, and novel crystals among evaluated methods, and maintains high compositional validity even under property conditioning.

Dylan John, Kim E. Jelfs, Alex M. Ganose +1

Department of Chemistry, Imperial College London · Department of Electrical and Electronic Engineering, Imperial College London

Constrained Generative Modeling Crystal Structure Generation Computational Materials Science

Oct 6, 2026cs.RO

Model-Based Geometry-Aware Generative Optimization for Constrained Locomotion Planning

Constrained Locomotion Planning (CLP) for quadrupeds and humanoids, where robots must satisfy collision avoidance, contact consistency, kinematic feasibility, and support constraints, is challenging under high-dimensional dynamics and highly non-convex environments. Recent Model-Based Diffusion (MBD) approaches recast trajectory optimization as posterior sampling over trajectories, using known dynamics and Monte Carlo rollouts to analytically estimate the denoising score function without demonstration learning. While constrained variants further incorporate feasibility into model-based score rollouts and show promising performance, they are still limited by (1) lacking a task-modulated active constraint geometry that shapes the score direction and reverse stochasticity, and (2) using deterministic DDPM-style reverse transport without adaptive scheduling across different generative transports. Therefore, we introduce Model-Based Geometry-Aware Generative Optimization (2GO) for constrained locomotion, which turns active constraint geometry into executable denoising operators through normal- induced metric shaping, tangent-space stochastic filtering, and CFS-based retraction. 2GO further decouples generative transport from reverse stochasticity through an adaptive diffusion and flow-like schedule. Experiments on constrained quadruped and humanoid locomotion demonstrate strong performance in discrete foothold selection and continuous posture planning, with higher success rates, fewer violations, and improved execution compatibility.

Zhilin He, Xinyuan Wang, Changliu Liu

Carnegie Mellon University · University of Michigan, Ann Arbor

Constrained Generative Modeling Constrained Motion Planning Humanoid Robot Locomotion Diffusion-Based Planning Model-Based Planning Quadruped Locomotion

Oct 5, 2026cs.LG

Constrained Goal-directed Planar Graph Generation with Grammar-based Reinforcement Learning

Planar graphs are central to applications across science and engineering, yet existing generators provide limited support for goal-directed generation under hard structural and geometric feasibility constraints. We propose a dataset-free method for generating planar graph embeddings by combining parametric graph grammars with safe reinforcement learning to optimize generic task-specific objectives while satisfying constraints during construction. We formulate the generation process as a constrained Markov decision process, where the graph grammar defines the state and action spaces. We further introduce an action projection that maps sampled actions toward state-dependent safe sets, improving constraint satisfaction during training. In contrast to classical graph generators and deep generative models, which typically offer limited goal-directed control or rely on weak constraint satisfaction, our method constructs feasible planar graph embeddings directly during generation. We also introduce a benchmark suite for constrained and goal-directed planar graph generation, together with classical and deep generative baselines. Across all benchmark tasks, our method consistently outperforms baselines while satisfying the formulated constraints.

Nicolas Hochuli, Lorenzo Miele, Kristina Shea +1

Engineering Design and Computing Laboratory ETH Zürich

Constrained Generative Modeling Graph Generation Constrained RL Generative Modeling

Oct 5, 2026cs.CV

AnchorGen: Anchored Optimization for Customizable Generative 3D Design

Engineering design often starts from a 2D sketch that fixes style and proportions, yet the subsequent 3D shape optimization relies on learned generative priors to keep the geometry valid. However, these priors are agnostic to the sketch: while they admit a valid design by correcting a drifted proposal back to its training distribution, they often correct it towards the high-density region, ignoring the specified design. We introduce \emph{AnchorGen}, a rectified-flow framework trained unconditionally on the concatenated shape and sketch latents of paired data. The learned manifold represents the joint distribution of shape-sketch pairs, so constraining the sketch component restricts the iterate to the sub-manifold of shapes consistent with a target style. Since training employs no conditioning signal, the constraint is imposed at inference: gradient descent optimizes the shape latent to minimize a differentiable drag surrogate, while constraining the sketch latent to remain close to the target sketch via a token-wise cosine penalty. A single model thereby supports design-preserving optimization, dimensionally explicit design edits, and sketch-only synthesis.

Hantao Zhang, Oliver Heinimann, Jieke Wu +3

CVLab, EPFL, Switzerland

Constrained Generative Modeling 3D Shape Editing 3D Shape Generation Flow-Based Generative Modeling

Oct 5, 2026cs.RO

Spacecraft Rendezvous Trajectory Generation with Modular Constraints via Diffusion Model Composition

Emerging mission classes such as on-orbit servicing, satellite inspection, and active debris removal require trajectory design methods that are adaptable to a variety of mission scenarios. We present a diffusion-based trajectory generation approach for rendezvous and proximity operations (RPO) that enables flexible configuration of mission constraints. First, individual energy-based diffusion models are trained to satisfy distinct constraints such as approach cone and sensor line-of-sight from a set of optimized trajectories. Then, at inference time, the learned energy models can be composed with one another, or with an analytically defined energy field, to enforce specific constraint combinations. We validate this framework with the composition of a learned approach cone model and a learned sensor line-of-sight model, as well as a learned approach cone model and synthetic obstacle avoidance model, both of which yield constraint satisfaction rates that are within 1 percentage point of the single-constraint models or higher. These results indicate that our compositional diffusion framework can provide a modular approach to RPO trajectory design and enable reconfiguration for new constraint combinations without requiring model retraining.

Mariko A. Storey-Matsutani, Richard Linares

Graduate Student, Department of Aeronautics and Astronautics, Massachusetts Inst. of Technology, Cambridge MA · Associate Professor, Department of Aeronautics and Astronautics, Massachusetts Inst. of Technology, Cambridge MA

Constrained Generative Modeling Trajectory Generation Diffusion-Based Planning Spacecraft Rendezvous and Proximity Operations Motion Planning Diffusion Models

Oct 1, 2026cs.CV

Moore, Escher, Penrose: A Conformal Golden Braid

I don't think I have ever done anything as peculiar in my life. Among other things, it shows a young man looking with interest at a print on the wall of an exhibition that features himself. How can this be? Perhaps I am not far removed from Einstein's curved universe.'' So wrote M.C. Escher about his 1956 lithograph Print Gallery. Nearly half a century later, a mathematical analysis related its geometry to an untwisted source image through a conformal power map

z \mapsto z^α

,

α\in \mathbb{C}

. Building on this construction, we use a frozen text-to-image diffusion model to generate new self-referential scenes. Prompting alone does not enforce the recursion, while a post-hoc transformation can leave structures poorly connected. Applying the transformation during sampling is also insufficient: the denoiser may "repair" the intended distortion or drift out of the prescribed geometry. We construct a generalized inverse

T^\dagger

of the non-invertible image transformation

T

, adapted to its recursive constraint. In the idealized formulation, the Penrose identity

TT^\dagger T = T

makes

TT^\dagger

an idempotent projection onto geometrically admissible images. Yet denoising only the transformed image remains an out-of-distribution task, even with projection. We therefore braid denoising steps with

T

and

T^\dagger

: source-space steps develop the untwisted scene, while transformed-space steps refine its appearance and connections in the final geometry. We generate Print Gallery-like compositions and explore further transformations. Rather than distorting a finished image, we let the scene and its distortion develop together.

Sophia Feldman, Assaf Shocher

Technion - Israel Institute of Technology

Constrained Generative Modeling Diffusion Model Guidance Image Generation T2I Diffusion Models

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, 2026cs.LG

EP-Flow: Disordered Crystal Structure Prediction without Site-Level Annotations

Generative models have made rapid progress in ordered crystal structure prediction, yet many functional materials are intrinsically disordered, with substitutional mixing, vacancies, or interstitial species controlling their properties. Existing crystal generators either assume deterministic site occupations or require site-level disorder annotations, which are often unavailable when the chemical formula is the primary input. We formulate disordered crystal structure prediction through an Occupancy Distribution Matrix (ODM), a continuous site-by-species representation that unifies ordered crystals, solid solutions, vacancy disorder, and interstitial occupancy. A valid ODM must satisfy coupled site-wise occupancy, mass-conservation, and non-negativity constraints, placing each sample on a formula-dependent transportation polytope. We propose Entropic Polytope Flow (EP-Flow), a marginal-constrained flow matching framework that canonicalizes heterogeneous polytopes into a shared double-centered space, learns a marginal-preserving flow, and recovers feasible occupancies through a Sinkhorn inverse map. By jointly generating occupancies, fractional coordinates, and lattice parameters, EP-Flow achieves state-of-the-art performance on formula-conditioned disordered CSP benchmarks derived from COD and MPDS, substantially outperforming adapted ordered-crystal generators. Analyses further show that EP-Flow recovers sparse and chemically meaningful local disorder patterns rather than merely matching global composition statistics.

Qiuliang Liu, Liming Wu, Qi Li +5

Institute of Physics, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China · Gaoling School of Artificial Intelligence, Renmin University of China

Constrained Generative Modeling Flow Matching Crystal Structure Prediction Computational Materials Science

Sep 30, 2026cs.LG

PMosFM: Preconditioned Manifold Matching for One-Step Physics-Constrained Generation

Physics-constrained generative models aim to generate physical fields that match a target distribution and satisfy prescribed constraints. However, enforcing these constraints often increases sampling costs through iterative corrections or training costs through residual optimization and trajectory unrolling. To address this issue, we introduce \textbf{P}reconditioned \textbf{M}anifold \textbf{o}ne-\textbf{s}tep \textbf{F}low \textbf{M}atching (\textbf{PMosFM}), a preconditioned manifold matching framework for one-step physics-constrained generation. By encoding constraints in a manifold decoder, PMosFM learns transport in intrinsic coordinates without separate residual losses or terminal residual unrolling. A geometric preconditioner rescales coordinates using the decoder-induced metric, while a regularized covariance transform approximately whitens the interpolation-state inputs. A finite-interval objective couples velocity supervision with consistency between decoded endpoints in physical space. We show that exact parameterization removes residual-induced Gauss--Newton curvature, that geometric and covariance effects separate in a local conditioning bound, and that physical flow-map error bounds endpoint distributional error. Controlled ablations examine conditioning, and experiments evaluate optimizer-update time and memory footprint. At inference, PMosFM uses one neural transport evaluation followed by physical decoding. Experiments across benchmarks show lower training and sampling time than the multi-step baselines at comparable physical and distributional fidelity. Code and datasets will be released publicly.

Zhangyong Liang, Haibin Ling

Department of Artificial Intelligence Westlake University

Constrained Generative Modeling Physics-Informed Generative Modeling Flow Matching One-Step Generative Modeling Flow-Based Generative Modeling

Sep 30, 2026cs.CL

Provably Tractable NFA-Constrained Language Generation via HMMs

Constrained generation aims to sample from language models (LMs) conditioned on hard constraints. Existing constrained-generation techniques for nondeterministic finite automaton (NFA) constraints either distort the distribution or sacrifice efficiency. Theoretically, this task reduces to counting the length-

n

sequences accepted by an NFA (#NFA), and the exact #NFA problem is #P-complete. Recent work has shown that #NFA admits a fully polynomial randomized approximation scheme (FPRAS). Inspired by this result, we propose NFA-LM, a polynomial-time engine for NFA-constrained generation with theoretical guarantees under mild assumptions. Experiments show that NFA-LM efficiently generates high-quality outputs with theoretically bounded approximation error.

Jialiang Sun, Kuldeep Meel

University of Toronto

Constrained Generative Modeling

Sep 30, 2026cs.LG

Fenchel Tilting: Weighted Correction for Efficient Finetuning of Generative Models

Adapting a pretrained generative model to an arbitrary preference expressed as a utility function underlies reward alignment, guided design, and constraint satisfaction, enabling diverse applications. Existing fine-tuning methods trade off generality against computational cost: they either restrict the family class of supported preferences to keep optimization simple or preserve generality at the expense of efficiency. We introduce Fenchel Tilt Flow Control (FTFC), which decouples utility optimization from generative-model fitting. FTFC first optimizes for a target distribution by jointly fitting an effective reward and density-ratio weights on pretrained samples. Method combines the utility's variational structure with Fenchel duality, supporting general

f

-divergence penalties that determine how rewards are transformed into an distribution-correction weights. These weights are then frozen and used to modify a diffusion or flow model in a single stage of importance-weighted denoising or flow matching, without differentiating through sampling trajectories. We establish exact duality for concave utilities under suitable conditions and show that weighted fitting reproduces the optimal target distribution for a given utility. Across image and molecule generation benchmarks, FTFC improves over baselines on diverse preference functions, while also being up to

20\times

more efficient. roposed method enables adaptation beyond expected-reward maximization without complex optimization, while preserving robustness for more general class of the utility functions compared to baselines.

Maksim Bobrin, Maksim Zhdanov, Dmitry Dylov

AXXX · Applied AI Institute · MBZUAI

Diffusion Model Alignment Constrained Generative Modeling Fine-Tuning Diffusion Model Fine-Tuning

Sep 29, 2026cs.LG

Synthesis Without Training: An Inference-Only Pipeline for Tabular, Temporal, and Relational Synthetic Data

Synthetic data generation is dominated by the fit-then-sample paradigm: a generative model is trained on a private dataset and then sampled from. Despite its widespread adoption, this paradigm faces three challenges: (1) a new training run is required for every dataset; (2) different data modalities, such as single tables, time series, and relational databases, require task-specific models and feature engineering; and (3) the resulting model is opaque, making its behavior under data constraints difficult to inspect. We propose GENSCRIPT, an inference-only pipeline that eliminates model training. GENSCRIPT computes a deterministic statistical profile of the source data (column types, ranges, missingness, categories, correlations, etc.) and passes it--rather than raw rows--to a language model to infer field semantics and cross-column integrity constraints. A coding agent then compiles the profile and constraints into an executable, auditable sampler. This unified approach supports single-table, temporal, and relational data without task-specific modeling. Across four single-table benchmarks, GENSCRIPT builds generators in 2 minutes and samples 50k rows within 6 seconds, while remaining within a few points of leading methods in marginal fidelity. Notably, it is the only method that perfectly preserves a 1-to-1 mapping between columns in the Adult dataset. On a smart-building dataset, it produces conditional time series that more closely match the real distribution than two baselines and perfectly preserves primary- and foreign-key relationships in the corresponding relational database.

Zilong Zhao, Abdul Raheem, Jiayu Li +5

Betterdata AI · National University of Singapore · University of Illinois Urbana-Champaign +1

Constrained Generative Modeling Synthetic Data Generation Time Series Generation LLM-Based Program Synthesis Synthetic Tabular Data Generation

Sep 29, 2026cs.LG

Multi-Agent Flow Matching with Decoupled Generative Guidance

Generative modeling is widely used for producing diverse objects from complex, multimodal distributions. However, its expressivity does not, in general, come with formal guarantees that the generated objects satisfy hard constraints or requirements. In multi-agent generation, this problem becomes more challenging because a hard requirement can depend on multiple agents, while each agent may need to determine its own guidance input without relying on the simultaneously computed guidance inputs of other agents. To this end, we introduce DeGG-Flow, a general framework for multi-agent flow matching with decoupled generative guidance. By representing the generative process as a control-affine dynamical system, we develop guidance conditions for two classes of coupled requirements: shared requirements whose satisfaction depends on multiple agents together, and private requirements associated with each individual agent dependent on its neighbors. For both classes, we establish feasibility conditions and finite-horizon convergence guarantees. We further derive a Wasserstein bound that characterizes the distributional deviation induced by the guidance. We demonstrate DeGG-Flow on multi-robot collaboration for crossing a spatial gap by reconfiguring the environment, and on multi-object scene generation with affordance requirements. Across both applications, DeGG-Flow directly generates objects that satisfy all corresponding hard requirements, including at team sizes unseen during training.

Ruoyu Lin, Magnus Egerstedt, Fabio Pasqualetti

Department of Electrical Engineering and Computer Science, University of California, Irvine, Irvine, CA 92697 USA · University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 USA

Constrained Generative Modeling Flow Matching Multi-Agent Collaboration Multi-Robot Coordination Flow-Based Generative Modeling

Sep 28, 2026cs.LG

Manifold-Stable Flow Matching

Flow matching (FM) learns generative dynamics through velocity regression. Geometric FM variants commonly assume a prior supported on the data manifold, requiring geometric knowledge that is often unavailable. Without such knowledge, low regression error alone does not guarantee manifold adherence. Adherence keeps generated samples within valid configurations and is empirically associated with better task performance. We introduce manifold-stable flow matching (MSFM), which can start from an arbitrary ambient prior, not necessarily supported on the manifold. Using tools from nonlinear dynamics, namely contraction theory, MSFM combines learned tangential transport with prescribed normal contraction. The construction uses analytical projectors for known manifolds and local affine proxies estimated by principal component analysis for unknown data geometry. By implementing contraction theory in both cases of known and unknown manifolds, we guarantee manifold invariance and transverse convergence to the manifold within a desired time window (e.g., one second). We derive a family of compatible probability paths and decompose the training loss into a learnable tangential term and a normal residual. An ellipse experiment attains a mean terminal off-manifold error of order

10^{-6}

. In Push-T robotic experiments, MSFM raises success from

74\%

to

82\%

. In the Robomimic Square task, success increases from

60\%

to

72\%

, while rotation-manifold deviation decreases from order

10^{-2}

to

10^{-7}

. The MSFM terminal geometric errors are controlled by the chosen numerical tolerance. These results demonstrate stronger geometric adherence and higher observed task performance, supporting prescribed normal contraction as a complement to learned generative transport.

Amirhossein Nazerian, Ali Pezeshki, Jianguo Zhao

Department of Mechanical Engineering Colorado State University Fort Collins, CO 80523, USA · Department of Electrical and Computer Engineering Colorado State University Fort Collins, CO 80523, USA

Constrained Generative Modeling Flow Matching Flow-Based Generative Modeling

Sep 28, 2026q-bio.BM

Continuous Variational Synthesis

Biological machine learning was long bottlenecked by the ability to synthesize designed DNA. Variational synthesis models control chemical reactions to physically manufacture quadrillions of designed sequences in DNA. However, training these generative models is challenging: constraints on chemical synthesis can force many parameters into a discrete space, limiting the ability to pre-train and fine-tune. In this article we train ``free'' variational synthesis models using stochastic gradient descent in continuous space, and then discretize with post-training quantization to impose hardware and wetware constraints. This enables variational synthesis models to satisfy stringent reward criteria, while still synthesizing diverse designs, achieving a strictly dominating quality-diversity Pareto frontier. We demonstrate by training variational synthesis models of enzymes, peptides, antibody CDRH3s, and regulatory DNA elements. In silico performance is maintained in vitro.

Alan N. Amin, Mattia G. Gollub, Andrei Slabodkin +2

JURA Bio, Inc. Boston, MA 02125, USA

Variational Autoencoders Constrained Generative Modeling Molecular Generation Protein Design

Sep 28, 2026cs.AI

Grab a Coffee: Future-Aware Guidance for Discrete Diffusion with Compiled Objectives

Discrete diffusion models generate sequences by iteratively resolving multiple tokens in parallel, offering a flexible alternative to left-to-right generation. However, guiding this process with a sequence-level objective is difficult because the value of one unresolved token depends on the other tokens with which it can form a high-reward sequence. Enumerating all such completions makes the whole guidance computation grow exponentially with the number of unresolved positions. We introduce COFFEE, a plug-and-play framework that avoids this enumeration by separating sequence dependence from the objective. At each diffusion step, a target-free carrier absorbs the marginal token distributions predicted by the denoiser to construct a joint model over the unresolved tokens, while a compiled finite-state model records how their combinations affect the sequence-level preference. Pairing their states allows COFFEE to transfer global preferences to unresolved positions and sample a clean reconstruction without retraining the diffusion model. The same framework supports explicit hard constraints and learned soft objectives. We evaluate COFFEE across multiple symbolic, language, and biological benchmarks, where it achieves strong control results with task-dependent quality and diversity trade-offs. By making objectives available to inference rather than only evaluation, COFFEE brings joint conditioning, completion-weighted guidance, and optimization-based constraints into pretrained neural generation, showing the potential of neural-symbolic methods in diffusion guidance.

Hua, Xu, Dongxin Li +4

Edward · Data Science and Analytics Thrust, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China · Department of Computer Science, University of California, Los Angeles, USA +1

Constrained Generative Modeling Diffusion Model Guidance Diffusion Models

Sep 28, 2026cs.CV

ConCAD: Constraint-Aware Image-to-CAD Generation with Dual-Granularity Rewards

Image-to-CAD generation seeks executable parametric programs that recover both the geometry and design intent of a reference object. Existing systems are commonly evaluated by validity and shape overlap, although two solids with similar volume can encode different CAD relations. We introduce ConCAD, a constraint-aware image-to-CAD framework optimized via Group Relative Policy Optimization (GRPO) with rewards at two complementary granularities: a code-level constraint reward and an execution-level geometric reward. This complementary design disambiguates structurally distinct yet volumetrically similar shapes while ensuring valid 3D geometry. To verify that these rewards recover geometry and design intent, we introduce a B-rep geometric constraint satisfaction rate (G-CSR), which analytically extracts and evaluates geometric constraints from boundary representations. Experiments on the DeepCAD and Zero2CAD demonstrate that ConCAD achieves the best IoU and Chamfer Distance over competitive baselines, while also outperforming them on G-CSR, validating its superior recovery of both geometric fidelity and parametric design intent.

Chenxi Zhai, Xi Cheng, Hang Cheng +5

Tsinghua University, Shenzhen International Graduate School

Constrained Generative Modeling 3D Asset Generation Parametric CAD Modeling

Sep 28, 2026cs.LG

Admissible Diffusion for Multimodal Interventional Trajectories

Generating a plausible clinical trajectory does not establish what would happen under a different treatment. We present ADMIT, a framework combining irregular multimodal representations, treatment-conditioned latent diffusion and explicit constraints on generated states or actions. We formulate its interventional target through sequential g-computation and distinguish causal assumptions from constraint satisfaction. Its admissibility mechanism translates physiological prior knowledge into explicit constraints on generated states and proposed actions. Treatment-exposure dynamics condition latent transitions, while state projection or action gating applies the constraints during rollout so that they influence subsequent trajectory generation. In our preliminary experiments, multimodal inputs improved supervised hidden-state recovery and reduced treatment-contrast error. In a simulated dosing-schedule experiment with leak-free history encoding, ADMIT predicted most of the tumor-volume change caused by redistributing a fixed total dose. An exposure input improved these predictions around a temporary dose reduction whether or not the assumed clearance rate was correct, but reduced the predicted size of a dose effect, and a deterministic recurrent baseline matched ADMIT's average predictions. Exposure projection reduced constraint violations, although enforcement remained incomplete. Semi-synthetic experiments using eICU context illustrated treatment-response generation under fixed and adaptive policies. Observational examples further characterize model treatment sensitivity. ADMIT provides a framework for testing whether complementary observations and physiological restrictions improve intervention trajectories, with representation recovery, effect accuracy and rule enforcement assessed separately.

Xing Han, Shravan Chaudhari, Jiarui Shao +2

Johns Hopkins University · Massachusetts Institute of Technology · Bayesian Health

Constrained Generative Modeling Causal Inference Longitudinal EHR Modeling Conditional Diffusion Models Multimodal Trajectory Prediction Trajectory Prediction

Sep 27, 2026cs.LG

SLP-ProbHard: Probabilistic Hard-Constrained Learning via Structural Latent Parameterization

Many probabilistic predictors must satisfy exact structure in every stochastic realization, yet common hard-constraint approaches form predictions in ambient coordinates and then correct or project them. We introduce SLP-ProbHard, a cross-family, representation-centered framework for probabilistic hard-constrained learning when explicit structural parameterizations are available. Its core object, a Structural Feasible Latent Parameterization (SFLP), combines a structural latent law

Z \sim P^Z_θ(\cdot\mid x)

with a feasible map

Y=h_φ(x,Z)

that satisfies the constraint for every latent realization. Together these components define the predictive law itself, including its support and boundary probabilities, rather than serving as a final feasibility wrapper. We study how feasible coordinates and maps affect stochastic dimension, dependence, calibration, expressiveness, and computation. Experiments use Gaussian latent laws and fixed geometry-derived maps across affine equalities, ordering and simplex constraints, nonlinear manifolds, and three structural representations of seven-basin hydrological flow-duration-curve (FDC) data. In an official-source affine comparison with ProbHardE2E/DPPL, both methods achieve zero practical constraint violations. SLP-ProbHard uses 8 instead of 11 stochastic coordinates and improves MSE/MAE, while DPPL yields better marginal CRPS and closer-to-nominal coverage; a paired test detects no Energy Score difference across ten seeds. Real-world affine and nonlinear FDC representations reduce 13 to 7 and 14 to 8 ambient versus computational coordinates, respectively. Exact feasibility alone thus does not determine a predictive law, motivating direct structural generation when meaningful feasible coordinates are available.

Wondesen Teshome Bekele, Marco D'Oria

Department of Engineering and Architecture, University of Parma, Parma, Italy · University School for Advanced Studies IUSS Pavia, Pavia, Italy

Constrained Generative Modeling Latent Variable Models Probabilistic Forecasting

Sep 27, 2026cs.LG

Source Anchoring for Physical Consistency in Flow Matching Models

Deep generative models are used to solve partial differential equations and model distributions of physical system states, but ensuring that the generated samples satisfy the governing laws remains challenging. Projection-based flow-matching methods enforce physics by correcting the flow from an unconstrained noise distribution. These corrections shift the generated samples away from the distribution of target solutions, especially in high noise regions. To address this limitation, we propose Source Anchoring for Physical Consistency (SAPC), a Functional Flow Matching method that encodes the physical constraints into the source noise before generation begins. We evaluate SAPC on five systems governed by partial differential equations, covering six tasks with linear and non-linear dynamics, and compare results against five baselines and the unconstrained backbone. Anchoring the source reduces the need for large corrections that drive samples onto admissible but off-distribution states, and SAPC reproduces the target distributions most accurately on every evaluated task, while matching the constraint precision of the best projection-based baselines. Ablation experiments show that this gain arises from pairing source projection with a matched training objective that regresses toward the projected source. These results identify the source distribution as a key design choice for physically consistent generative modelling.

Giulia Romoli, Filippo Ruffini, Paolo Soda

Department of Diagnostics and Intervention, Ume˚a University, Sweden · Unit of Artificial Intelligence and Computer Systems, Universit`a Campus Bio-Medico di Roma, Italy

Constrained Generative Modeling Physics-Informed Generative Modeling Flow Matching Generative Modeling Flow-Based Generative Modeling

Sep 24, 2026cs.LG

From Graphs to Feeders: Constraint-Guided Diffusion for Rule-Compliant Feeder Generation

Generative modeling approaches often focus on recovering broad statistical characteristics from the training data. In the context of graph generation, this may refer to degree distributions, clustering coefficients, or spectral properties. However, generating usable distribution feeders when detailed feeder models are unavailable requires more than matching generic graph statistics: the sampled topology must also obey electrical compatibility and radiality rules. We therefore formulate feeder synthesis as a constraint-guided graph generation problem and propose the Power-Grid-constrained Discrete Denoising Diffusion model, PG-DiGress, which learns categorical node and edge patterns from feeder data, while respecting domain-specific rules. Specifically, it injects feeder constraints into the reverse diffusion process through soft masks that suppress incompatible edge classes during denoising, followed by a final projection step that rebuilds a connected, rule-compliant feeder graph. We evaluate PG-DiGress using graph-distribution similarity, feeder-rule satisfaction, structural validity, and downstream model construction. Compared with the unconstrained baseline, PG-DiGress increases the strict feeder pass rate from 13.7% to 96.8%. We also successfully convert the generated graphs into executable feeder models for downstream analysis.

Yu Qin, Andrew Glaws, Aadil Latif +1

National Laboratory of the Rockies, Golden, Colorado, USA

Constrained Generative Modeling Diffusion Models Graph Diffusion Power Systems

Sep 14, 2026cs.LG

Backward SDEs-based Diffusion for Physics-Constrained Generation

Pretrained score-based diffusion models provide strong unconditional priors, yet enforcing measurement or physics consistency in inverse problems is often handled by heuristic guidance, intermittent projections, or task-specific conditional training, with limited guarantees of feasibility at the end of inference. We propose terminal-conditioned inversion for score-based SDE priors. Given a frozen Score-SDE prior and a task-defined terminal feasibility specification, we construct an associated backward stochastic differential equation whose adapted solution defines a principled inverse map from the terminal requirement to a prior state at a chosen noise level. Under standard regularity conditions, we establish existence and uniqueness of the adapted solution and obtain terminal consistency by construction. We further develop a practical neural BSDE solver that composes arbitrary pretrained diffusion priors with domain constraints without modifying the score-defined coefficients, producing an anchored prior state that enables neighborhood sampling for uncertainty characterization. Experiments on toy datasets validate stable terminal-conditioned inversion and distributionally consistent neighborhood sampling. As a real-world case study, we apply the framework to sparse-view CT reconstruction and achieve improved reconstruction quality over representative training-free baselines while satisfying strict measurement feasibility under the prescribed terminal specification. Project is available in: https://laplace.center/icmlbsdeI/

Zihao Wang

Diffusion Model Inversion Constrained Generative Modeling Stochastic Differential Equations Diffusion-Based Inverse Problems Image Inverse Problems

Sep 8, 2026cs.LG

Let It Go or Learn to Self-Correct: Continuous Diffusion for Constrained Discrete Tasks

Denoising Diffusion Probabilistic Models (DDPMs) generate samples by starting from noise and repeatedly denoising while keeping each update close to the current noisy state. This behavior is effective in many continuous domains, but its role is less clear for globally constrained discrete tasks, such as Sudoku, graph connectivity, Latin squares, and N-queens. In such settings, early discrete errors can be difficult to undo. As a result, standard diffusion sampling may preserve early mistakes, even when the model's clean predictions are informative. We compare standard samplers to sampling directly from the model's clean prediction. Without retraining, this single change improves Sudoku validity from 31% to 95%, with consistent gains across the other discrete tasks. We hypothesize that staying close to the current noisy state is harmful because the reverse trajectory can drift off the forward noising distribution the model was trained on. To reduce this train-test mismatch, we further introduce self-correction training, which exposes the model to its own predictions, improving robustness to errors that arise during inference. This substantially improves the performance of standard samplers. Our results suggest that continuous diffusion models can learn nontrivial global constraints, but discrete reasoning tasks require better alignment between training and inference: either through samplers that reduce commitment to early decisions, or through training that teaches the model to correct its own inference-time errors.

Mariia Drozdova, Stéphane Liem Nguyen, François Fleuret

University of Geneva

Constrained Generative Modeling Diffusion Sampling Diffusion Models

Sep 8, 2026cs.LG

Geodesic-informed Generative Diffusion Model For Topology-preserved Image Video Generation

Generative diffusion models have emerged as a class of powerful techniques for various imaging applications, including but not limited to synthesis, reconstruction, and segmentation. Despite their success, current generative models pose two key limitations. First, they primarily rely on image intensity and texture information, with limited attention to underlying object geometry. As a result, they do not guarantee geometric or topological consistency during the generation process, which is a crucial requirement for high-stakes domains such as computational anatomy, biology, and robotics, where preserving object structure is critical. Second, existing models fail to explicitly learn or represent shape changes in the generative process. Such deformation dynamics remain occluded within network parameters; hence leaving the transformation process uninterpretable and physically uninformed. To address these challenges, we introduce IGG (Image Generation informed by Geodesic dynamics), a novel framework that integrates topology-preserving geodesic principles into the diffusion-based generative process. In contrast to conventional methods that operate in image intensity space, IGG learns and synthesizes diverse samples within geodesic deformation spaces, where geometric object changes are learned as smooth and invertible smooth mappings from a given template/source image. Our code is publicly available at https://github.com/nellie689/IGG.

Nian Wu, Nivetha Jayakumar, Jiarui Xing +1

University of Virginia, Department of Electrical & Computer Engineering, Charlottesville, VA, USA · Yale School of Medicine, New Haven, CT, USA · University of Virginia, Department of Computer Science, Charlottesville, VA, USA

Constrained Generative Modeling Image Generation Diffusion Models

Sep 7, 2026cs.CL

BlueprintAgent: Constraint-Triggered Targeted Revisits for Simulation-Ready Generation from Scanned Structural Blueprints

Converting in-service reinforced-concrete (RC) building blueprints into simulation-ready models---structured frame representations that support deterministic FEM export and qualified-engineer review---underpins safety assessment and seismic retrofit, but the process remains manual. Direct prompting of a multimodal large language model (MLLM) over a scanned sheet is unreliable: outputs often violate engineering constraints on beam--column support, span count, or 3D continuity. We present BlueprintAgent (BPA), a constraint-triggered multimodal agent for simulation-ready frame extraction from scanned blueprints. BPA treats the MLLM as the primary reader and decision maker, with OCR and computer vision supplying localized evidence. Its central mechanism realizes engineering constraints as callable validators whose entity-level conflict reports trigger targeted MLLM revisits over the local region---an inference-time control distinct from fixed pipelines and free-form self-reflection. We evaluate BPA on 300 real scanned blueprint sheets from 20 anonymized RC frame projects, against five baselines and six ablations. BPA reaches a macro-averaged Beam F1 of 0.994, against 0.301 for single-MLLM zero-shot and 0.820 for a fixed pipeline; removing MLLM-led axis adjudication collapses Beam and Column F1 on complex multi-sheet projects. For dense technical drawings, engineering constraints are best deployed as triggers for entity-level targeted revisits rather than as post-hoc output filters.

Zhouyuan Xu, Chen Yang, Linhao Wang +2

Tsinghua University, Beijing 100084, China

Document Understanding Constrained Generative Modeling Multimodal Agents

Sep 3, 2026cs.CV

Fill My Mirror: Geometry-Constrained Mirror Inpainting

Mirrors are common in real-world images, yet producing geometrically consistent reflections with generative models remains challenging. Unlike most objects, mirror appearance depends on scene geometry and viewpoint, making it hard to synthesize using learned appearance priors alone. We address this in the mirror inpainting setting, where the scene is fixed and only the mirror region is generated. Our key insight is that much mirror content is geometrically constrained by the visible scene and need not be hallucinated. We estimate scene geometry and project visible content into the mirror to recover reflection regions determined by geometry. A generative model then completes the mirror region via a two-mask diffusion strategy balancing geometric constraints with the model's learned priors, reducing projection artifacts and improving reflection consistency. The method is training-free and applicable to complex real-world scenes. We evaluate on MirrorBench-V2 (synthetic) and real images. Using standard and geometry-aware metrics, we show that explicitly using scene geometry improves consistency.

Ofek Basson, Shimon Vainer, Yacov Hel-Or +1

Reichman University

Constrained Generative Modeling Image Inpainting

Aug 31, 2026q-fin.CP

Latent-Space No-Arbitrage Geometry of Generative Models for Implied Volatility Surfaces

Generative models for implied volatility surfaces must produce outputs that satisfy static no-arbitrage constraints. We study these constraints in latent space. For a fixed generator, we assign each latent code a scalar margin determined by the no-arbitrage conditions of the generated surface. The codes with nonnegative margin form the admissible latent set. We establish conditions under which strictly admissible codes remain admissible under small perturbations and the boundary of the admissible set is characterized by zero margin. For regular boundary components, we formulate a level-set equation whose local dynamics are directed toward the zero-margin set. The analysis treats the generator as a map from latent variables to surfaces and is therefore not restricted to a particular architecture. It applies to variational autoencoders, generative adversarial networks, and other generative models with a deterministic realization map. Numerical tests recover known boundaries in analytic examples. Experiments with a variational autoencoder trained on Heston surfaces show that similar reconstruction errors can correspond to different admissible regions and that the latent prior may be concentrated inside such a region. The computed boundary can also be used to modify latent codes that generate violating surfaces.

Jing Wang, Shuaiqiang Liu, Cornelis Vuik

Delft Institute of Applied Mathematics, Delft University of Technology

Constrained Generative Modeling Neural Representation Geometry Quantitative Finance