Constrained Generative Modeling

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Constrained generative modeling studies how to generate useful samples while respecting requirements such as grammatical rules, molecular validity, physical laws, or safe trajectories. Common approaches include grammar and automaton-based decoding, diffusion and flow-matching methods with projections or primal-dual guidance, and models that build constraints into their representations or training objectives. Applications range from structured text and synthetic data to molecules, motion planning, scientific fields, and engineering design, with evaluation often balancing constraint satisfaction against sample quality, diversity, and computational cost. A central challenge is that enforcing feasibility does not necessarily preserve the model’s intended distribution or uncertainty, so methods must limit bias while remaining efficient and reliable under complex constraints.

Latest papers

192 papers50 papers in the last four weeks, up 163% on the four weeks before. 0.3% of all new papers.

May 16, 2026

Constrained Code Generation with Discrete Diffusion

Discrete diffusion models are a powerful, emerging paradigm for code generation. They construct programs through iterative refinement of partially corrupted token sequences and enable parallel token refinement. Importantly, this paradigm exposes a global program state at each denoising step, which provides a natural intervention point for enforcing program-level functionality and security constraints, guiding the generation before the final code is committed. Building on this observation, the paper introduces Constrained Diffusion for Code (CDC), a training-free neurosymbolic inference framework that integrates constraint satisfaction directly into the reverse denoising process. CDC augments the base discrete diffusion sampler with constraint-aware denoising operators that combine mathematical optimization with program analysis to identify constraint-relevant regions of the intermediate program state and locally adjust the denoising trajectory, steering generation toward feasible programs while remaining close to the base model. Across code generation benchmarks, CDC consistently improves constraint satisfaction in functional correctness, security, and even syntax, outperforming discrete diffusion and autoregressive baselines with less corrective computation and more localized edits.

Lize Shao, Michael Cardei, Zichen Xie +2

University of Virginia

Constrained Generative Modeling Constrained Decoding Code Generation Secure Code Generation Diffusion Models

May 15, 2026

StippleDiffusion: Capacity-Constrained Stippling using Controlled Diffusion

Stipple patterns, point sets whose local density tracks a target image, are traditionally produced by per-density iterative optimizers, which are slow, non-differentiable, and must be re-run from scratch for each new target. Learned alternatives have so far addressed only unconditional point generation; capacity-constrained, image-conditioned stippling has remained out of reach. We present the first diffusion-based sampler that simultaneously satisfies a learned local point-distribution prior and a continuous, image-defined capacity constraint at inference. The method is a ControlNet branch built on top of an optimal-transport-grid point-set diffusion baseline, conditioned on the target density map and a high-resolution image. Two design choices make the combination tractable: training and inference are restricted to the late-stage denoising regime, initialized from a density-weighted rejection sample, and the standard zero-convolution injection is replaced with a sigmoid-gated 1x1 projection that preserves the base model's blue-noise structure under hard density signals. A single trained checkpoint accepts arbitrary target densities at inference, generalizes to point budgets that were not seen during training, and produces stipples in time nearly independent of the output point count. On the Icons-50 benchmark, our learned sampler reaches parity with per-density-optimized baselines on every reported metric while remaining differentiable end-to-end.

Ofir Gilad, Aleksander Plocharski, Przemyslaw Musialski +1

Ben Gurion University of the Negev, Israel · Warsaw University of Technology, and Akces NCBR, Poland · New Jersey Institute of Technology, United States

Constrained Generative Modeling Diffusion Sampling Generative Modeling Conditional Diffusion Models

May 13, 2026

Generative Floor Plan Design with LLMs via Reinforcement Learning with Verifiable Rewards

An AI system for professional floor plan design must precisely control room dimensions and areas while respecting the desired connectivity between rooms and maintaining functional and aesthetic quality. Existing generative approaches focus primarily on respecting the requested connectivity between rooms, but do not support generating floor plans that respect numerical constraints. We introduce a text-based floor plan generation approach that fine-tunes a large language model (LLM) on real plans and then applies reinforcement learning with verifiable rewards (RLVR) to improve adherence to topological and numerical constraints while discouraging invalid or overlapping outputs. Furthermore, we design a set of constraint adherence metrics to systematically measure how generated floor plans align with user-defined constraints. Our model generates floor plans that satisfy user-defined connectivity and numerical constraints and outperforms existing methods on Realism, Compatibility, and Diversity metrics. Across all tasks, our approach achieves at least a 94% relative reduction in Compatibility compared with existing methods. Our results demonstrate that LLMs can effectively handle constraints in this setting, suggesting broader applications for text-based generative modeling.

Luis Lara, Aristides Milios, Zhi Hao Luo +5

Mila – Quebec AI Institute · Université de Montréal · Polytechnique Montréal +1

Constrained Generative Modeling Generative Modeling Floor Plan Generation Indoor Scene Generation

May 13, 2026

Learning Local Constraints for Reinforcement-Learned Content Generators

Constraint-based game content generators that learn local constraints from existing content, such as Wave Function Collapse (WFC), can generate visually satisfying game levels but face challenges in optimizing global properties, such as playability. On the other hand, reinforcement-learning-trained generators can optimize global properties---because such properties can easily be included in reward functions---but the results can be visually dissatisfying. In this paper, we explore ways to combine these methods. Specifically, we constrain the action space of a PCGRL generator with constraints learned by WFC, effectively allowing the PCGRL generator to achieve global properties while being forced to adhere to local constraints. To better analyze how this hybrid content generation method operates, we vary the number and type of inputs, and we test whether to randomly collapse the starting state and exclude rare patterns. While the method is sensitive to hyperparameter tuning, the best of our trained generators produce visually satisfying and playable puzzle-platform game levels---such as Lode Runner levels---with desired global properties.

Debosmita Bhaumik, Julian Togelius, Georgios N. Yannakakis +1

Institute of Digital Games, Msida, Malta · Game Innovation Lab, New York, New York, USA

Constrained Generative Modeling Constrained RL Generative Modeling Procedural Content Generation RL for Generative Models

May 12, 2026

Constraint-Aware Flow Matching: Decision Aligned End-to-End Training for Constrained Sampling

Deep generative models provide state-of-the-art performance across a wide array of applications, with recent studies showing increasing applicability for science and engineering. Despite a growing corpus of literature focused on the integration of physics-based constraints into the generation process, existing approaches fail to enforce strict constraint satisfaction while maintaining sample quality. In particular, training-free constrained sampling methods, while providing per-sample feasibility guarantees, introduce a fundamental mismatch between the training objective and the constrained sampling procedure, often leading to performance degradation. Identifying this training-sampling misalignment as a central limitation of current constrained generative modeling approaches, this paper proposes Constraint-Aware Flow Matching, a novel end-to-end framework that explicitly incorporates constraint projections into the training objective. By aligning the model's learned dynamics with the constrained sampling process, the proposed method mitigates distributional shift induced by projection-based corrections, enabling high-quality constrained generation. The proposed approach is evaluated on three challenging real-world benchmarks, illustrating the generality and efficacy of the method.

Jacob K. Christopher, James E. Warner, Ferdinando Fioretto

University of Virginia · NASA Langley Research Center

Constrained Generative Modeling Flow Matching Generative Modeling Flow-Based Generative Modeling Constrained Sampling

May 11, 2026

Enforcing Constraints in Generative Sampling via Adaptive Correction Scheduling

Hard constraints in generative sampling are typically enforced by projection, applied either once at the end of sampling or after every update. This binary framing overlooks a fundamental issue: projection changes the distribution of states which future updates depend on. As a result, delayed projection can produce samples that are feasible but inconsistent with the intended sampling dynamics, even after final projection. We formalize constraint enforcement as a correction scheduling problem over the generative rollout. Using one-step constraint defect as a local signal of geometric mismatch, we introduce adaptive correction scheduling, a state-dependent policy that allocates projection budget to the steps that most strongly perturb the trajectory. Terminal and stepwise projection arise as limiting cases of this family. Across controlled manifold rollouts and a learned projected diffusion sampler, adaptive scheduling improves the cost-accuracy frontier at matched projection budgets, recovering 71.2% of full stepwise benefit with 75% fewer corrections. These results show that constraint timing is a first-class design variable in generative sampling, and that enforcing feasibility alone is insufficient to preserve the intended constrained sampling dynamics.

Noah Trupin, Yexiang Xue

Department of Computer Science, Purdue University

Constrained Generative Modeling Diffusion Sampling Generative Modeling Constrained Sampling

May 10, 2026

Primal-Dual Guided Decoding for Constrained Discrete Diffusion

Discrete diffusion models generate structured sequences by progressively unmasking tokens, but enforcing global property constraints during generation remains an open challenge. We propose primal-dual guided decoding, an inference-time method that formulates constrained generation as a KL-regularised optimisation problem and solves it online via adaptive Lagrangian multipliers. At each denoising step, the method modifies token logits through an additive, constraint-dependent bias, with multipliers updated by mirror descent based on constraint violation. The bias arises as the optimal KL-regularised projection of the constraint, so the constrained distribution remains as close as possible to the model's unconstrained distribution while still satisfying the constraint. The method requires no retraining and no additional model evaluations beyond standard sampling, supports multiple simultaneous constraints, and provides formal bounds on constraint violation. We evaluate our approach on topical text generation, molecular design, and music playlist generation, showing that a single algorithm instantiated via domain-specific scoring functions improves constraint satisfaction while preserving relevant domain-specific quality metrics.

Federico Tomasi, Dmitrii Moor, Alice Wang +1

Spotify

Primal-Dual Optimization Constrained Generative Modeling Constrained Decoding Diffusion Guidance Constrained Optimization Diffusion Models+1

May 8, 2026

Towards Highly-Constrained Human Motion Generation with Retrieval-Guided Diffusion Noise Optimization

Generating human motion that satisfies customized zero-shot goal functions, enabling applications such as controllable character animation and behavior synthesis for virtual agents, is a critical capability. While current approaches handle many unseen constraints, they fail on tasks with very challenging spatiotemporal restrictions, such as severe spatial obstacles or specified numbers of walking steps. To equip motion generators for these highly constrained tasks, we present a retrieval-guided method built on the training-free diffusion noise optimization framework. The key idea is to search within large motion datasets for guidance that can potentially satisfy difficult constraints. We introduce relational task parsing to group target constraints and identify the difficult ones to be handled by retrieved reference. A better initialization for diffusion noise is then obtained via a reward-guided mask that combines random noise with retrieved noise. By optimizing diffusion noise from this improved initialization, we successfully solve highly constrained generation tasks. By leveraging LLM for relational task parsing, the whole framework is further enabled to automatically reason for what to retrieve, improving the intelligence of moving agents under a training-free optimization scheme.

Hanchao Liu, Fang-Lue Zhang, Shining Zhang +2

Tsinghua University · University of New South Wales

Constrained Generative Modeling Retrieval-Augmented Generation Diffusion Guidance Human Motion Generation Diffusion Models for Motion Generation

May 8, 2026

Exact Regular-Constrained Variable-Order Markov Generation via Sparse Context-State Belief Propagation

Variable-order Markov models generate sequences over a finite alphabet by conditioning each symbol on the longest available suffix of the generated history. Regular constraints, by contrast, describe finite-horizon control requirements by an automaton: fixed positions, forced endings, metrical patterns, and forbidden copied fragments are all special cases. Existing exact methods already handle regular constraints with belief propagation for first-order Markov chains. The contribution here is the variable-order extension: identifying the state space on which the existing BP-regular machinery must be run when the generator is a variable-order/backoff model. A first-order constraint layer can enforce useful support conditions, but it computes future mass after merging histories that a variable-order generator deliberately keeps distinct. We formalize this mismatch and give the sparse construction obtained by replacing the first-order Markov state with the observed context state, then taking the standard product with the regular constraint automaton. For a fixed trained context graph and automaton, inference is linear in the sequence horizon; in general it is polynomial in the number of reachable product edges. This gives the correct variable-order distribution conditioned on regular constraints without expanding to all K-tuples. The same finite-source interface supports reversible data augmentation by inverse count lookup, matching materialized transposition augmentation without storing transformed corpora. We also separate exact BP inference from generation-time backoff policies, such as singleton avoidance, whose stochastic semantics must be made explicit if exactness is claimed.

François Pachet

LIP6, Sorbonne Université · Ynosound

Constrained Generative Modeling Belief Propagation Constrained Decoding Markov Models Sequence Modeling

Apr 26, 2026

FlowPlace: Flow Matching for Chip Placement

Chip placement plays an important role in physical design. While generative models like diffusion models offer promising learning-based solutions, current methods have the following limitations: they use random synthetic data for pre-training, require long sampling times, and often result in overlaps due to their dependence on gradient-based solvers during the sampling process. To overcome these issues, we propose FlowPlace, which features mask-guided synthetic data generation, flow-based efficient training with flexible prior injection, and hard constraint sampling for overlap-free layouts. Experiments on OpenROAD and ICCAD 2015 benchmarks show FlowPlace achieves better PPA metrics, 10-50

\times

faster sampling efficiency, and zero overlaps.

Peng Xie, Ke Xue, Yunqi Shi +6

1State Key Laboratory of Novel Software Technology, Nanjing University, China · School of Artificial Intelligence, Nanjing University, China · 3Huawei Noah’s Ark Lab, China

Constrained Generative Modeling Flow Matching Electronic Design Automation Generative Modeling Flow-Based Generative Modeling

Apr 24, 2026

BrickNet: Graph-Backed Generative Brick Assembly

We train a language model to generate LEGO-brick build sequences. While prior work has been restricted to discrete, voxel-like towers, we consider a much broader set of pieces, encompassing thousands of part types with diverse connection semantics. To enable this, we first collect a large-scale dataset of over 100,000 human-designed LDraw brick objects and scenes. The complexity of our setting makes it challenging to autoregressively assemble structures that satisfy physical constraints. When predicting block pose directly, build sequences quickly become invalid after a small number of steps. Although pieces are placed in 3D space, it is the spatial relationships of the parts which define the whole. With this in mind, we design a graph-based program representation that parametrizes structure through connectivity, improving the physical grounding of generated sequences. To enable future applications, we make our dataset and models available for research purposes. https://kulits.github.io/BrickNet

Peter Kulits, Cordelia Schmid

Inria, `Ecole Normale Sup`erieure, CNRS, PSL Research University · Max Planck Institute for Intelligent Systems, Tübingen

Constrained Generative Modeling 3D Asset Generation Generative Modeling

Apr 20, 2026

UniCSG: Unified High-Fidelity Content-Constrained Style-Driven Generation via Staged Semantic and Frequency Disentanglement

Style transfer must match a target style while preserving content semantics. DiT-based diffusion models often suffer from content-style entanglement, leading to reference-content leakage and unstable generation. We present UniCSG, a unified framework for content-constrained, style-driven generation in both text-guided and reference-guided settings. UniCSG employs staged training: (i) a latent-space semantic disentanglement stage that combines low-frequency preprocessing with conditioning corruption to encourage content-style separation, and (ii) a latent-space frequency-aware detail reconstruction stage that refines details via multi-scale frequency supervision. We further incorporate pixel-space reward learning to align latent objectives with perceptual quality after decoding. Experiments demonstrate improved content faithfulness, style alignment, and robustness in both settings.

Jingwei Yang, Ruoxi Wu, Wei Shen +4

China University of Mining and Technology, Beijing, China · OPPO Artificial Intelligence Center, Beijing, China

Constrained Generative Modeling Diffusion Transformer Image Style Transfer Representation Disentanglement Diffusion-Based Image Generation Controllable Image Generation

Apr 20, 2026

Efficient Diffusion Models under Nonconvex Equality and Inequality constraints via Landing

Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for constrained diffusion models on generic nonconvex feasible sets

Σ

that simultaneously enforces equality and inequality constraints throughout the diffusion process. Our framework incorporates both overdamped and underdamped dynamics for forward and backward sampling. A key algorithmic innovation is a computationally efficient landing mechanism that replaces costly and often ill-defined projections onto

Σ

, ensuring feasibility without iterative Newton solves or projection failures. By leveraging underdamped dynamics, we accelerate mixing toward the prior distribution, effectively alleviating the high simulation costs typically associated with constrained diffusion. Empirically, this approach reduces function evaluations and memory usage during both training and inference while preserving sample quality. On benchmarks featuring equality and mixed constraints, our method achieves comparable sample quality to state-of-the-art baselines while significantly reducing computational cost, providing a practical and scalable solution for diffusion on nonconvex feasible sets.

Kijung Jeon, Michael Muehlebach, Molei Tao

Georgia Institute of Technology · Max Planck Institute for Int. Sys.

Constrained Generative Modeling Langevin Dynamics Diffusion Model Sampling Diffusion Model Inference Acceleration Diffusion Models Constrained Sampling

Apr 17, 2026

DALM: A Domain-Algebraic Language Model via Three-Phase Structured Generation

Large language models compress heterogeneous knowledge into a single parameter space, allowing facts from different domains to interfere during generation. We propose DALM, a Domain-Algebraic Language Model that replaces unconstrained token generation with structured denoising over a domain lattice. DALM follows a three-phase generation path: it first resolves domain uncertainty, then relation uncertainty, and finally concept uncertainty, so each stage operates under explicit algebraic constraints. The framework requires only three ingredients: a lattice of domains with computable meet, join, and implication; a typing function over relations that controls inheritance across domains; and a fiber partition that localizes knowledge to domain-specific subsets. Given these ingredients, DALM yields a three-phase encoder-decoder architecture in which generation is confined to a domain fiber, cross-domain contamination is structurally prevented in closed-vocabulary mode and auditably bounded in open-vocabulary mode, and a single query can produce a domain-indexed multi-perspective answer space. We instantiate the framework with the CDC knowledge representation system and outline training and evaluation on validated domain-annotated crystal libraries. DALM reframes language generation as algebraically constrained structured denoising rather than unconstrained decoding over a flat token space.

Chao Li

Constrained Generative Modeling Knowledge Conflicts in Language Models Controllable Text Generation Knowledge Representation Language Modeling Conditional Generative Modeling

Apr 16, 2026

Schema-Key Wording as an Instruction Channel in Structured Generation under Constrained Decoding

Constrained decoding is widely used to make large language models produce structured outputs that satisfy schemas such as JSON. Existing work mainly treats schemas as structural constraints, overlooking that schema-key tokens also enter the autoregressive context and may guide generation. To the best of our knowledge, we present the first systematic study of schema keys as an implicit instruction channel under constrained decoding. We formulate structured generation as a multi-channel instruction problem, where task signals can be placed in prompts, schema keys, or both. We further provide a projection-aware analysis that gives a sufficient condition under which an unconstrained expected-score advantage of an instructional key is preserved after grammar projection. Experiments on GSM8K and Math500 across seven language models show that changing only schema-key wording can substantially affect accuracy, with both positive and negative effects across models. Prompt-level and schema-level instructions also interact non-additively. The evidence is substantially stronger on GSM8K than on Math500. Our findings show that schema design is not merely output formatting, but part of instruction specification in structured generation.

Yifan Le

Independent Researcher

Constrained Generative Modeling Constrained Decoding LLM Prompting Text Generation Grammar-Constrained Decoding Schema-Constrained Generation

Apr 14, 2026

Conflated Inverse Modeling to Generate Diverse and Temperature-Change Inducing Urban Vegetation Patterns

Urban areas are increasingly vulnerable to thermal extremes driven by rapid urbanization and climate change. Traditionally, thermal extremes have been monitored using Earth-observing satellites and numerical modeling frameworks. For example, land surface temperature derived from Landsat or Sentinel imagery is commonly used to characterize surface heating patterns. These approaches operate as forward models, translating radiative observations or modeled boundary conditions into estimates of surface thermal states. While forward models can predict land surface temperature from vegetation and urban form, the inverse problem of determining spatial vegetation configurations that achieve a desired regional temperature shift remains largely unexplored. This task is inherently underdetermined, as multiple spatial vegetation patterns can yield similar aggregated temperature responses. Conventional regression and deterministic neural networks fail to capture this ambiguity and often produce averaged solutions, particularly under data-scarce conditions. We propose a conflated inverse modeling framework that combines a predictive forward model with a diffusion-based generative inverse model to produce diverse, physically plausible image-based vegetation patterns conditioned on specific temperature goals. Our framework maintains control over thermal outcomes while enabling diverse spatial vegetation configurations, even when such combinations are absent from training data. Altogether, this work introduces a controllable inverse modeling approach for urban climate adaptation that accounts for the inherent diversity of the problem. Code is available at the GitHub repository.

Baris Sarper Tezcan, Hrishikesh Viswanath, Rubab Saher +1

Computer Science Purdue University, West Lafayette, IN, USA · Forestry and Natural Resources Purdue University, West Lafayette, IN, USA

Inverse Design Constrained Generative Modeling Diffusion-Based Inverse Problems Conditional Generative Modeling Urban Planning

Apr 13, 2026

Generative Design for Direct-to-Chip Liquid Cooling for Data Centers

Rapid growth in artificial intelligence (AI) workloads is driving up data center power densities, increasing the need for advanced thermal management. Direct-to-chip liquid cooling can remove heat efficiently at the source, but many cold plate channel layouts remain heuristic and are not optimized for the strongly non-uniform temperature distribution of modern heterogeneous packages. This work presents a generative design framework for synthesizing cooling channel geometries for the NVIDIA GB200 Grace Blackwell Superchip. A physics-based finite-difference thermal model provides rapid steady-state temperature predictions and supplies spatial thermal feedback to a constrained reaction-diffusion process that generates novel channel topologies while enforcing inlet/outlet and component constraints. By iterating channel generation and thermal evaluation in a closed loop, the method naturally redistributes cooling capacity toward high-power regions and suppresses hot-spot formation. Compared with a baseline parallel channel design, the resulting channels achieve more than a 5 degree Celsius reduction in average temperature and over 35 degree Celsius reduction in maximum temperature. Overall, the results demonstrate that coupling generative algorithms with lightweight physics-based modeling can significantly enhance direct-to-chip liquid cooling performance, supporting more sustainable scaling of AI computing.

Zheng Liu

University of Michigan-Dearborn Dearborn, MI

Physics-Informed Generative Modeling Constrained Generative Modeling

Apr 12, 2026

Learning and Enforcing Context-Sensitive Control for LLMs

Controlling the output of Large Language Models (LLMs) through context-sensitive constraints has emerged as a promising approach to overcome the limitations of Context-Free Grammars (CFGs) in guaranteeing generation validity. However, such constraints typically require manual specification -- a significant barrier demanding specialized expertise. We introduce a framework that automatically learns context-sensitive constraints from LLM interactions through a two-phase process: syntactic exploration to gather diverse outputs for constraint learning, followed by constraint exploitation to enforce these learned rules during generation. Experiments demonstrate that our method enables even small LLMs (1B parameters) to learn and generate with perfect constraint adherence, outperforming larger counterparts and state-of-the-art reasoning models. This work represents the first integration of context-sensitive grammar learning with LLM generation, eliminating manual specification while maintaining generation validity.

Mohammad Albinhassan, Pranava Madhyastha, Mark Law +1

Imperial College London · City University of London · The Alan Turing Institute +1

Constrained Generative Modeling Grammar-Constrained Decoding

Apr 11, 2026

CircuitSynth: Reliable Synthetic Data Generation

The generation of high-fidelity synthetic data is a cornerstone of modern machine learning, yet Large Language Models (LLMs) frequently suffer from hallucinations, logical inconsistencies, and mode collapse when tasked with structured generation. Existing approaches, such as prompting or retrieval-augmented generation, lack the mechanisms to balance linguistic expressivity with formal guarantees regarding validity and coverage. To address this, we propose CircuitSynth, a novel neuro-symbolic framework that decouples semantic reasoning from surface realization. By distilling the reasoning capabilities of a Teacher LLM into a Probabilistic Sentential Decision Diagram (PSDD), CircuitSynth creates a tractable semantic prior that structurally enforces hard logical constraints. Furthermore, we introduce a convex optimization mechanism to rigorously satisfy soft distributional goals. Empirical evaluations across diverse benchmarks demonstrate that CircuitSynth achieves 100% Schema Validity even in complex logic puzzles where unconstrained baselines fail (12.4%) while significantly outperforming state-of-the-art methods in rare-combination coverage.

Zehua Cheng, Wei Dai, Jiahao Sun +1

Department of Computer Science, University of Oxford · Institute of Logic and Computation, TU Wien

Synthetic Data Generation Synthetic Data Generation for Language Models Constrained Generative Modeling Neuro-Symbolic Reasoning

Apr 9, 2026

What a Comfortable World: Ergonomic Principles Guided Apartment Layout Generation

Current data-driven floor plan generation methods often reproduce the ergonomic inefficiencies found in real-world training datasets. To address this, we propose a novel approach that integrates architectural design principles directly into a transformer-based generative process. We formulate differentiable loss functions based on established architectural standards from literature to optimize room adjacency and proximity. By guiding the model with these ergonomic priors during training, our method produces layouts with significantly improved livability metrics. Comparative evaluations show that our approach outperforms baselines in ergonomic compliance while maintaining high structural validity.

Piotr Nieciecki, Aleksander Plocharski, Przemyslaw Musialski

Warsaw University of Technology, Poland · Akces NCBR, Poland · New Jersey Institute of Technology, United States of America

Floor Plan Generation Generative Modeling Indoor Scene Generation Constrained Generative Modeling

Apr 9, 2026

Coordinate-Based Dual-Constrained Autoregressive Motion Generation

Text-to-motion generation has attracted increasing attention in the research community recently, with potential applications in animation, virtual reality, robotics, and human-computer interaction. Diffusion and autoregressive models are two popular and parallel research directions for text-to-motion generation. However, diffusion models often suffer from error amplification during noise prediction, while autoregressive models exhibit mode collapse due to motion discretization. To address these limitations, we propose a flexible, high-fidelity, and semantically faithful text-to-motion framework, named Coordinate-based Dual-constrained Autoregressive Motion Generation (CDAMD). With motion coordinates as input, CDAMD follows the autoregressive paradigm and leverages diffusion-inspired multi-layer perceptrons to enhance the fidelity of predicted motions. Furthermore, a Dual-Constrained Causal Mask is introduced to guide autoregressive generation, where motion tokens act as priors and are concatenated with textual encodings. Since there is limited work on coordinate-based motion synthesis, we establish new benchmarks for both text-to-motion generation and motion editing. Experimental results demonstrate that our approach achieves state-of-the-art performance in terms of both fidelity and semantic consistency on these benchmarks.

Kang Ding, Hongsong Wang, Jie Gui +1

School of Cyber Science and Engineering, Southeast University, Nanjing 210096, China · School of Computer Science and Engineering, Key Laboratory of New Generation Artificial Intelligence Technology and Its Interdisciplinary Applications, Ministry of Education, Southeast University, Nanjing 210096, China · School of Cyber Science and Engineering, Southeast University, also with Purple Mountain Laboratories, Nanjing 211111, China, and also with Engineering Research Center of Blockchain Application, Supervision And Management (Southeast University), Ministry of Education, Southeast University, Nanjing 210096, China +1

Text-to-Motion Generation Human Motion Generation Constrained Generative Modeling

Apr 9, 2026

Hidden Biases in Conditioning Autoregressive Models

Large language and music models are increasingly used for constrained generation: rhyming lines, fixed meter, inpainting or infilling, positional endings, and other global form requirements. These systems often perform strikingly well, but the induced procedures are usually not exact conditioning of the underlying autoregressive model. This creates a hidden inferential bias, distinct from the better-known notion of bias inherited from the training set: samples are distorted relative to the true constrained distribution, with no generic guarantee of complete coverage of the admissible solution space or of correct conditional probabilities over valid completions. We formalize several exact inference tasks for autoregressive models and prove corresponding hardness results. For succinctly represented autoregressive models whose next-token probabilities are computable in polynomial time, exact sentence-level maximum a posteriori (MAP) decoding is NP-hard. This hardness persists under unary and metrical constraints. On the sampling side, exact conditioned normalization is #P-hard even for regular constraints such as fixed-length terminal events. Unlike finite-state Markov models, general autoregressive models do not admit a bounded-state dynamic program for these tasks. These results formalize a standard claim in the neural decoding literature: local autoregressive sampling is easy, whereas exact decoding and exact conditioning under global form constraints are computationally intractable in general.

Francois Pachet, Pierre Roy

LIP6, Sorbonne Université · Soundtrap

Constrained Generative Modeling Constrained Decoding Autoregressive Language Modeling Autoregressive Modeling

Apr 8, 2026

ExplainFuzz: Explainable and Constraint-Conditioned Test Generation with Probabilistic Circuits

Understanding and explaining the structure of generated test inputs is essential for effective software testing and debugging. Existing approaches--including grammar-based fuzzers, probabilistic Context-Free Grammars (pCFGs), and Large Language Models (LLMs)--suffer from critical limitations. They frequently produce ill-formed inputs that fail to reflect realistic data distributions, struggle to capture context-sensitive probabilistic dependencies, and lack explainability. We introduce ExplainFuzz, a test generation framework that leverages Probabilistic Circuits (PCs) to learn and query structured distributions over grammar-based test inputs interpretably and controllably. Starting from a Context-Free Grammar (CFG), ExplainFuzz compiles a grammar-aware PC and trains it on existing inputs. New inputs are then generated via sampling. ExplainFuzz utilizes the conditioning capability of PCs to incorporate test-specific constraints (e.g., a query must have GROUP BY), enabling constrained probabilistic sampling to generate inputs satisfying grammar and user-provided constraints. Our results show that ExplainFuzz improves the coherence and realism of generated inputs, achieving significant perplexity reduction compared to pCFGs, grammar-unaware PCs, and LLMs. By leveraging its native conditioning capability, ExplainFuzz significantly enhances the diversity of inputs that satisfy a user-provided constraint. Compared to grammar-aware mutational fuzzing, ExplainFuzz increases bug-triggering rates from 35% to 63% in SQL and from 10% to 100% in XML. These results demonstrate the power of a learned input distribution over mutational fuzzing, which is often limited to exploring the local neighborhood of seed inputs. These capabilities highlight the potential of PCs to serve as a foundation for grammar-aware, controllable test generation that captures context-sensitive, probabilistic dependencies.

Annaëlle Baiget, Jaron Maene, Seongmin Lee +3

UCLA, USA · KU Leuven, Belgium

Automated Test Generation Constrained Generative Modeling Generative Modeling

Apr 7, 2026

ReLU Networks for Exact Generation of Similar Graphs

Generation of graphs constrained by a specified graph edit distance from a source graph is important in applications such as cheminformatics, network anomaly synthesis, and structured data augmentation. Despite the growing demand for such constrained generative models in areas including molecule design and network perturbation analysis, the neural architectures required to provably generate graphs within a bounded graph edit distance remain largely unexplored. In addition, existing graph generative models are predominantly data-driven and depend heavily on the availability and quality of training data, which may result in generated graphs that do not satisfy the desired edit distance constraints. In this paper, we address these challenges by theoretically characterizing ReLU neural networks capable of generating graphs within a prescribed graph edit distance from a given graph. In particular, we show the existence of constant depth and O(n^2 d) size ReLU networks that deterministically generate graphs within edit distance d from a given input graph with n vertices, eliminating reliance on training data while guaranteeing validity of the generated graphs. Experimental evaluations demonstrate that the proposed network successfully generates valid graphs for instances with up to 1400 vertices and edit distance bounds up to 140, whereas baseline generative models fail to generate graphs with the desired edit distance. These results provide a theoretical foundation for constructing compact generative models with guaranteed validity.

Mamoona Ghafoor, Tatsuya Akutsu

Bioinformatics Center, Institute for Chemical Research, Department of Intelligence Sciences and Technology, Kyoto University, Uji 611-0011, Japan

Graph Generation Constrained Generative Modeling ReLU Neural Networks

Apr 3, 2026

Physics-Constrained Adaptive Flow Matching for Climate Downscaling

Regional climate information at kilometer scales is essential for assessing the impacts of climate change, but generating it with global climate models is too expensive due to their high computational costs. Machine learning models offer a fast alternative, yet they often violate basic physical laws and degrade when applied to climates outside of their training distribution. We present Physics-Constrained Adaptive Flow Matching (PC-AFM), a generative downscaling model that addresses both problems. Building on the Adaptive Flow Matching (AFM) model of Fotiadis et al. (2025) as our baseline, we add soft conservation constraints that keep the downscaled output consistent with the large-scale input for precipitation and humidity, and use gradient surgery via the ConFIG algorithm to prevent these constraints from interfering with the generative objective. We train the model on Central Europe climate data, evaluate it on a 10-time downscaling task (63km to 6.3km) over six variables (near-surface temperature, precipitation, specific humidity, surface pressure, and horizontal wind components) across a comprehensive set of metrics including bias, ensemble skill scores, power spectra, and conservation error, and test the generalization on two held-out climate regions. Within the training distribution, PC-AFM reduces conservation errors and improves ensemble calibration while matching the baseline on standard skill metrics. Outside the training distribution, where unconstrained models develop large systematic errors by extrapolating learned statistics, PC-AFM halves precipitation wet bias, reduces conservation error and improves extreme-quantile accuracy, all without any information about the target climate at inference time. These results indicate that physical consistency is a practical requirement for deploying generative downscaling models in real-world applications.

Kevin Debeire, Aytaç Paçal, Pierre Gentine +3

Deutsches Zentrum für Luft- und Raumfahrt (DLR), Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany · School of Computation, Information and Technology, Technical University of Munich, Germany · LEAP Center, Columbia University, New York, NY, 10027, USA +1

Climate Downscaling Physics-Informed Generative Modeling Constrained Generative Modeling Precipitation Downscaling Flow Matching OOD Generalization

Apr 3, 2026

Generating DDPM-based Samples from Tilted Distributions

Given

n

independent samples from a

d

-dimensional probability distribution, our aim is to generate diffusion-based samples from a distribution obtained by tilting the original, where the degree of tilt is parametrized by

θ\in \mathbb{R}^d

. We define a plug-in estimator and show that it is minimax-optimal. We develop Wasserstein bounds between the distribution of the plug-in estimator and the true distribution as a function of

n

and

θ

, illustrating regimes where the output and the desired true distribution are close. Further, under some assumptions, we prove the TV-accuracy of running Diffusion on these tilted samples. Our theoretical results are supported by extensive simulations. Applications of our work include finance, weather and climate modelling, and many other domains, where the aim may be to generate samples from a tilted distribution that satisfies practically motivated moment constraints.

Himadri Mandal, Dhruman Gupta, Rushil Gupta +5

Indian Statistical Institute, Kolkata. · Ashoka University. · Tata Institute of Fundamental Research +2

Diffusion Sampling Constrained Generative Modeling

Apr 3, 2026

HiDiGen: Hierarchical Diffusion for B-Rep Generation with Explicit Topological Constraints

Boundary representation (B-rep) is the standard 3D modeling format in CAD systems, encoding both geometric primitives and topological connectivity. Despite its prevalence, deep generative modeling of valid B-rep structures remains challenging due to the intricate interplay between discrete topology and continuous geometry. In this paper, we propose HiDiGen, a hierarchical generation framework that decouples geometry modeling into two stages, each guided by explicitly modeled topological constraints. Specifically, our approach first establishes face-edge incidence relations to define a coherent topological scaffold, upon which face proxies and initial edge curves are generated. Subsequently, multiple Transformer-based diffusion modules are employed to refine the geometry by generating precise face surfaces and vertex positions, with edge-vertex adjacencies dynamically established and enforced to preserve structural consistency. This progressive geometry hierarchy enables the generation of more novel and diverse shapes, while two-stage topological modeling ensures high validity. Experimental results show that HiDiGen achieves strong performance, generating novel, diverse, and topologically sound CAD models.

Shurui Liu, Weide Chen, Ancong Wu

School of Computer Science and Engineering, Sun Yat-sen University, China · School of Intelligent Systems Engineering, Shenzhen Campus of Sun Yat-sen University, China

3D Shape Generation Constrained Generative Modeling 3D Diffusion Models

Apr 2, 2026

Generative models on phase space

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be concentrated on a submanifold of the data embedding space. For high-energy physics data, consisting of collections of relativistic energy-momentum 4-vectors, this submanifold can enforce extremely strong physically-motivated priors, such as energy and momentum conservation. If these constraints are learned only approximately, rather than exactly, this can inhibit the interpretability and reliability of such generative models. To remedy this deficiency, we introduce generative models which are, by construction, confined at every step of their sampling trajectory to the manifold of massless N-particle Lorentz-invariant phase space in the center-of-momentum frame. In the case of diffusion models, the "pure noise" forward process endpoint corresponds to the uniform distribution on phase space, which provides a clear starting point from which to identify how correlations among the particles emerge during the reverse (de-noising) process. We demonstrate that our models are able to learn both few-particle and many-particle distributions with various singularity structures, paving the way for future interpretability studies using generative models trained on simulated jet data.

Zachary Bogorad, Ibrahim Elsharkawy, Yonatan Kahn +2

Theory Division, Fermi National Accelerator Laboratory, Batavia, IL, USA · Department of Physics, University of Toronto and Vector Institute, Toronto, ON, Canada and NERSC, Lawrence Berkeley National Laboratory, Berkeley, California, USA · Department of Physics, University of Toronto and Vector Institute, Toronto, ON, Canada +2

Generative Modeling Constrained Generative Modeling Physics-Informed Generative Modeling Diffusion Models High-Energy Physics

Apr 2, 2026

AeroTherm-GPT: A Verification-Centered LLM Framework for Thermal Protection System Engineering Workflows

Integrating Large Language Models (LLMs) into hypersonic thermal protection system (TPS) design is bottlenecked by cascading constraint violations when generating executable simulation artifacts. General-purpose LLMs, treating generation as single-pass text completion, fail to satisfy the sequential, multi-gate constraints inherent in safety-critical engineering workflows. To address this, we propose AeroTherm-GPT, the first TPS-specialized LLM Agent, instantiated through a Constraint-Closed-Loop Generation (CCLG) framework. CCLG organizes TPS artifact generation as an iterative workflow comprising generation, validation, CDG-guided repair, execution, and audit. The Constraint Dependency Graph (CDG) encodes empirical co-resolution structure among constraint categories, directing repair toward upstream fault candidates based on lifecycle ordering priors and empirical co-resolution probabilities. This upstream-priority mechanism resolves multiple downstream violations per action, achieving a Root-Cause Fix Efficiency of 4.16 versus 1.76 for flat-checklist repair. Evaluated on HyTPS-Bench and validated against external benchmarks, AeroTherm-GPT achieves 88.7% End-to-End Success Rate (95% CI: 87.5-89.9), a gain of +12.5 pp over the matched non-CDG ablation baseline, without catastrophic forgetting on scientific reasoning and code generation tasks.

Chuhan Qiao, Jinglai Zheng, Jie Huang +3

School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, China · Beijing Research Institute of Telemetry, Beijing, 100076, China

LLM Agent Workflow Optimization Constrained Generative Modeling Program Synthesis Code Generation

Mar 31, 2026

iPoster: Content-Aware Layout Generation for Interactive Poster Design via Graph-Enhanced Diffusion Models

We present iPoster, an interactive layout generation framework that empowers users to guide content-aware poster layout design by specifying flexible constraints. iPoster enables users to specify partial intentions within the intention module, such as element categories, sizes, positions, or coarse initial drafts. Then, the generation module instantly generates refined, context-sensitive layouts that faithfully respect these constraints. iPoster employs a unified graph-enhanced diffusion architecture that supports various design tasks under user-specified constraints. These constraints are enforced through masking strategies that precisely preserve user input at every denoising step. A cross content-aware attention module aligns generated elements with salient regions of the canvas, ensuring visual coherence. Extensive experiments show that iPoster not only achieves state-of-the-art layout quality, but offers a responsive and controllable framework for poster layout design with constraints.

Xudong Zhou, Jinyuan Liang, Qiuyi Guo +1

Beijing Institute of Technology, Beijing, China

Constrained Generative Modeling Diffusion Models