Generative Modeling

In generative modeling, we often wish to produce samples that maximize a user-specified reward such as aesthetic quality or alignment with human preferences, a problem known as guidance. Despite their widespread use, existing guidance methods either require expensive multi-particle, many-step schemes or rely on poorly understood approximations. We reformulate guidance as a deterministic optimal control problem, yielding a hierarchy of algorithms that subsumes existing approaches at the coarsest level. We show that the flow map, an object of significant recent interest for its role in fast inference, arises naturally in the optimal solution. Based on this observation, we propose Flow Map Reward Guidance (FMRG): a training-free, single-trajectory framework that uses the flow map to both integrate and guide the flow. At text-to-image scale, FMRG matches or surpasses baselines across inverse problems and reward-guided generation with as few as 3 NFEs, giving at least an order-of-magnitude speedup in comparison to prior state of the art. Code is available at https://github.com/jrrhuang/fmrg.

Large Language Models (LLMs) have shown strong potential for narrative generation, but their use in complex, multi-layered role-playing game (RPG) worlds is still limited by issues of coherence, controllability, and structural consistency. This paper explores a dependency-aware, multi-stage prompt pipeline for procedural RPG content generation that models narrative dependencies through structured intermediate representations. The approach decomposes generation into sequential stages: world building, non-player character creation, player character creation, campaign-level quest planning, and quest expansion. Each stage conditions on structured JSON outputs from previous stages. By enforcing schemas and explicit data flow, the pipeline reduces narrative drift, limits hallucinations, and supports scalable creation of interconnected narrative elements. The system is evaluated qualitatively through human-centered analysis across multiple independent runs. Outputs are assessed using criteria such as structural completeness, internal consistency, narrative coherence, diversity, and actionability. Results show that the pipeline consistently generates logically sound and structurally valid RPG content, without quality degradation as complexity increases. Separating high-level campaign planning from detailed quest expansion improves both global structure and local storytelling. These findings suggest that dependency-aware prompt pipelines with structured intermediate representations are an effective design pattern for LLM-based procedural content generation. This approach may also generalize to other domains requiring sequential reasoning over evolving contextual states.

Ultra-reliable and low-latency communication (URLLC) will play a key role in fifth-generation (5G) and beyond networks, enabling mission-critical applications. Meeting the stringent URLLC requirements, characterized by extremely low packet error rates and minimal latency, calls for advanced statistical modeling to accurately capture rare events in wireless channels. Traditional methods, such as those that rely on large datasets and computationally intensive estimation techniques, often fail in real-time scenarios. In this paper, a novel framework is proposed to meet URLLC requirements through a synergistic integration of extreme value theory (EVT) with generative artificial intelligence (AI). EVT is used to model channel tail distributions, providing an accurate characterization of rare events. Concurrently, generative AI enables data augmentation and channel parameter estimation from limited samples. The integration of EVT with generative AI can thus help overcome the limitations of generative models in capturing extreme events during channel characterization. Using an experimental dataset collected from an automotive environment, it is demonstrated that this integration enhances data augmentation for extreme quantiles, while requiring fewer samples than traditional analytical EVT methods and generative baselines in online estimation of channel distribution.

Learning matrix-valued distributions from high-dimensional and possibly incomplete training data is challenging: ambient-space generative modeling is computationally expensive and statistically fragile when the matrix dimension is large but the sample size is limited. We propose CoreFlow, a geometry-preserving low-rank flow model that learns shared row/column subspaces across the matrix distribution, and then trains a continuous normalizing flow only on the induced low-dimensional core. CoreFlow is designed for settings where shared low-rank matrix geometry is present, especially in high-dimensional limited-sample regimes. This separates shared matrix geometry from sample-specific variation, preserves matrix structure, and substantially improves training efficiency. The same framework also handles incomplete training matrices through masked Riemannian updates and iterative completion. Across real and synthetic benchmarks, CoreFlow substantially improves spectral and moment-level generation quality in few-sample regimes while remaining competitive in data-rich settings, even under compression to 9% of the ambient dimension and with up to 40% missing training entries.

This paper studies the identifiability and stability of drifting fields in the framework of Generative Modeling via Drifting. The motivating question is whether a zero-drift equilibrium identifies the target distribution and whether an approximately vanishing drift implies weak distributional convergence. Since the original drifting model employs the Laplace kernel by default, we first analyze why Gaussian score-based arguments fail to apply. This analysis motivates the introduction of companion-elliptic kernel families, which are characterized by a companion potential satisfying an elliptic closure relation. We show that this class naturally contains the Laplace kernel and consists precisely of Gaussian and Matérn kernels with smoothness parameter $ν>0$. Within this class, we establish field identifiability for arbitrary Borel probability measures on $R^d$: if the drifting field between two such measures vanishes identically, then they must coincide. For stability, we demonstrate that convergence of the field alone does not guarantee weak convergence, since mass may escape to infinity while remaining invisible to the field. Although tightness directly removes this obstruction and restores weak stability, we prove that, even without tightness, every $C_0$-vague cluster point lies exactly on the defect ray $\{cp:0\le c\le1\}$. Consequently, a single scalar $C_0$ observable suffices to detect the missing mass and recover weak convergence.

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.

Deep generative models and neural operators have demonstrated significant potential for 3D aerodynamic inference. However, they often face inherent challenges in maintaining physical consistency and preserving high-frequency features, primarily due to spectral bias and gradient conflicts within the governing equations. To address these issues, we propose GeoFunFlow-3D, a physics-guided generative flow matching framework. Temporally, we utilize optimal transport theory to build the generation path, ensuring stable training dynamics. Spectrally, we introduce a high-order discrete engine without automatic differentiation (No-AD) to reduce gradient stiffness. Spatially, a topology-aware super-resolution module (SATO) is employed to rigorously enforce physical laws in localized regions such as shock waves. We evaluated our framework on complex industrial datasets. On the BlendedNet dataset, the model successfully avoids mode collapse even under sparse data conditions. For the NASA Rotor37 test, it accurately captures 3D detached shock structures. Compared to conventional operators, GeoFunFlow-3D significantly improves accuracy, reducing the pressure field error (RRMSE) to 0.0215 while maintaining competitive inference efficiency. Ultimately, this work provides a reliable, geometry-driven approach for generating high-dimensional fluid fields.

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

Diffusion-based generative models have reformed generative AI, and also enabled new capabilities in the science domain, e.g., fast generation of 3D structures of molecules. In such tasks, there is often a symmetry in the system, identifying elements that can be converted by certain transformations as equivalent. Equivariant diffusion models guarantee a symmetric distribution, but miss the opportunity to make learning easier, while alignment-based simplification attempts fail to preserve the target distribution. In this work, we develop quotient-space diffusion models, a principled generative framework to fully handle and leverage symmetry. By viewing the intrinsic generation process on the quotient space, the exact construction that removes symmetry redundancy, the framework simplifies learning by allowing model output to have an arbitrary intra-equivalence-class movement, while generating the correct symmetric target distribution with guarantee. We instantiate the framework for molecular structure generation which follows $\mathrm{SE}(3)$ (rigid-body movement) symmetry. It improves the performance over equivariant diffusion models and outperforms alignment-based methods universally for small molecules and proteins, representing a new framework that surpasses previous symmetry treatments in generative models.

Rings like gold, thuds like wood! The sound we hear in a scene is shaped not only by the spatial layout of the environment but also by the materials of the objects and surfaces within it. For instance, a room with wooden walls will produce a different acoustic experience from a room with the same spatial layout but concrete walls. Accurately modeling these effects is essential for applications such as virtual reality, robotics, architectural design, and audio engineering. Yet, existing methods for acoustic modeling often entangle spatial and material influences in correlated representations, which limits user control and reduces the realism of the generated acoustics. In this work, we present a novel approach for material-controlled Room Impulse Response (RIR) generation that explicitly disentangles the effects of spatial and material cues in a scene. Our approach models the RIR using two modules: a spatial module that captures the influence of the spatial layout of the scene, and a material module that modulates this spatial RIR according to a user-specified material configuration. This explicitly disentangled design allows users to easily modify the material configuration of a scene and observe its impact on acoustics without altering the spatial structure or scene content. Our model provides significant improvements over prior approaches on both acoustic-based metrics (up to +16% on RTE) and material-based metrics (up to +70%). Furthermore, through a human perceptual study, we demonstrate the improved realism and material sensitivity of our model compared to the strongest baselines.

Latent Diffusion Models (LDMs) achieve high-fidelity synthesis but suffer from latent space brittleness, causing discontinuous semantic jumps during editing. We introduce a Riemannian framework to diagnose this instability by analyzing the generative Jacobian, decomposing geometry into Local Scaling (capacity) and Local Complexity (curvature). Our study uncovers a **Geometric Decoupling"**: while curvature in normal generation functionally encodes image detail, OOD generation exhibits a functional decoupling where extreme curvature is wasted on unstable semantic boundaries rather than perceptible details. This geometric misallocation identifies Geometric Hotspots" as the structural root of instability, providing a robust intrinsic metric for diagnosing generative reliability.

Drifting Models [Deng et al., 2026] train a one-step generator by evolving samples under a kernel-based drift field, avoiding ODE integration at inference. The original analysis leaves two questions open. The drift-field iteration admits a locally repulsive regime in a two-particle surrogate, and vanishing of the drift ($V_{p,q}\equiv 0$) is not known to force the learned distribution $q$ to match the target $p$. We derive a contraction threshold for the surrogate and show that a linearly-scheduled friction coefficient gives a finite-horizon bound on the error trajectory. Under a Gaussian kernel we prove that the drift-field equilibrium is identifiable: vanishing of $V_{p,q}$ on any open set forces $q=p$, closing the converse of Proposition 3.1 of Deng et al. Our friction-augmented model, DMF (Drifting Model with Friction), matches or exceeds Optimal Flow Matching on FFHQ adult-to-child domain translation at 16x lower training compute.

In principle, deep generative models can be used to perform domain adaptation; i.e. align the input feature representations of test data with that of a separate discriminative model's training data. This can help improve the discriminative model's performance on the test data. However, generative models are prone to producing hallucinations and artefacts that may degrade the quality of generated data, and therefore, predictive performance when processed by the discriminative model. While uncertainty quantification can provide a means to assess the quality of adapted data, the standard framework for evaluating the quality of predicted uncertainties may not easily extend to generative models due to the common lack of ground truths (among other reasons). Even with ground truths, this evaluation is agnostic to how the generated outputs are used on the downstream task, limiting the extent to which the uncertainty reliability analysis provides insights about the utility of the uncertainties with respect to the intended use case of the adapted examples. Here, we describe how decision-theoretic uncertainty quantification can address these concerns and provide a convenient framework for evaluating the trustworthiness of generated outputs, in particular, for domain adaptation. We consider a case study in photoplethysmography time series denoising for Atrial Fibrillation classification. This formalises a well-known heuristic method of using a downstream classifier to assess the quality of generated outputs.

Recent generative AI models have achieved remarkable breakthroughs in language and visual understanding. However, although these models can generate realistic visual content, their spatial scale remains confined to bounded environments, preventing them from capturing how geographic environments evolve across thousands of kilometers or from modeling the spatial structure of the large-scale physical world. This limitation poses a critical challenge for ultra-wide-area spatial intelligence in Earth observation and simulation, revealing a deeper gap in generative AI: progress has relied primarily on scaling model parameters and training data, while overlooking spatial scale as a core dimension of intelligence. Here, motivated by this missing dimension, we investigate spatial scale as a new scaling axis in foundation models and present MetaEarth3D, the first generative foundation model capable of spatially consistent generation at the planetary scale. Taking optical Earth observation simulation as a testbed, MetaEarth3D enables the generation of multi-level, unbounded, and diverse 3D scenes spanning large-scale terrains, medium-scale cities, and fine-grained street blocks. Built upon 10 million globally distributed real-world training images, MetaEarth3D demonstrates both strong visual realism and geospatial statistical realism. Beyond generation, MetaEarth3D serves as a generative data engine for diverse virtual environments in ultra-wide spatial intelligence. We argue that this study may help empower next-generation spatial intelligence for Earth observation.

Steering intermediate representations has emerged as a powerful strategy for controlling generative models, particularly in post-deployment alignment and safety settings. However, despite its empirical success, it currently lacks a comprehensive theoretical framework. In this paper, we bridge this gap by formalizing the theory of concept steering. First, we establish a link between steering and affine concept erasure, proving that the standard approach for removing unwanted behaviors is a special case of LEACE (a closed-form method for affine erasure). Next, we formulate a principled theoretical framework for concept switching, LEACE-Switch, and characterize the assumptions under which it provides an optimal affine solution. Building on this analysis, we then introduce MidSteer (Minimal Disturbance concept Steering), a more general affine framework for concept manipulation that relaxes these assumptions and enables directed, minimal-disturbance transformations. We demonstrate that MidSteer performs favorably across a range of tasks, modalities, and architectures, including vision diffusion models and large language models.

The success of deep generative models in generating high-quality and diverse samples is often attributed to particular architectures and large training datasets. In this paper, we investigate the impact of these factors on the quality and diversity of samples generated by flow-matching models. Surprisingly, in our experiments on CelebA-HQ dataset, flow matching remains stable even when pruning 50% of the dataset. That is, the quality and diversity of generated samples are preserved. Moreover, pruning impacts the latent representation only slightly, that is, samples generated by models trained on the full and pruned dataset map to visually similar outputs for a given seed. We observe similar stability when changing the architecture or training configuration, such that the latent representation is maintained under these changes as well. Our results quantify just how strong this stability can be in practice, and help explain the reliability of flow-matching models under various perturbations.

Analyzing unsteady fluid flows often requires access to the full distribution of possible temporal states, yet conventional PDE solvers are computationally prohibitive and learned time-stepping surrogates quickly accumulate error over long rollouts. Generative models avoid compounding error by sampling states independently, but diffusion and flow-matching methods, while accurate, are limited by the cost of many evaluations over the entire mesh. We introduce scale-autoregressive modeling (SAR) for sampling flows on unstructured meshes hierarchically from coarse to fine: it first generates a low-resolution field, then refines it by progressively sampling higher resolutions conditioned on coarser predictions. This coarse-to-fine factorization improves efficiency by concentrating computation at coarser scales, where uncertainty is greatest, while requiring fewer steps at finer scales. Across unsteady-flow benchmarks of varying complexity, SAR attains substantially lower distributional error and higher per-sample accuracy than state-of-the-art diffusion models based on multi-scale GNNs, while matching or surpassing a flow-matching Transolver (a linear-time transformer) yet running 2-7x faster than this depending on the task. Overall, SAR provides a practical tool for fast and accurate estimation of statistical flow quantities (e.g., turbulent kinetic energy and two-point correlations) in real-world settings.

While the manifold hypothesis is widely adopted in modern machine learning, complex data is often better modeled as stratified spaces -- unions of manifolds (strata) of varying dimensions. Stratified learning is challenging due to varying dimensionality, intersection singularities, and lack of efficient models in learning the underlying distributions. We provide a deep generative approach to stratified learning by developing two generative frameworks for learning distributions on stratified spaces. The first is a sieve maximum likelihood approach realized via a dimension-aware mixture of variational autoencoders. The second is a diffusion-based framework that explores the score field structure of a mixture. We establish the convergence rates for learning both the ambient and intrinsic distributions, which are shown to be dependent on the intrinsic dimensions and smoothness of the underlying strata. Utilizing the geometry of the score field, we also establish consistency for estimating the intrinsic dimension of each stratum and propose an algorithm that consistently estimates both the number of strata and their dimensions. Theoretical results for both frameworks provide fundamental insights into the interplay of the underlying geometry, the ambient noise level, and deep generative models. Extensive simulations and real dataset applications, such as molecular dynamics, demonstrate the effectiveness of our methods.

Affective Image Manipulation (AIM) aims to evoke specific emotions through targeted editing. Current image editing benchmarks primarily focus on object-level modifications in general scenarios, lacking the fine-grained granularity to capture affective dimensions. To bridge this gap, we introduce the first benchmark designed for AIM termed AIM-Bench. This benchmark is built upon a dual-path affective modeling scheme that integrates the Mikels emotion taxonomy with the Valence-Arousal-Dominance framework, enabling high-level semantic and fine-grained continuous manipulation. Through a hierarchical human-in-the-loop workflow, we finally curate 800 high-quality samples covering 8 emotional categories and 5 editing types. To effectively assess performance, we also design a composite evaluation suite combining rule-based and model-based metrics to holistically assess instruction consistency, aesthetics, and emotional expressiveness. Extensive evaluations reveal that current editing models face significant challenges, most notably a prevalent positivity bias, which stemming from inherent imbalances in training data distribution. To tackle this, we propose a scalable data engine utilizing an inverse repainting strategy to construct AIM-40k, a balanced instruction-tuning dataset comprising 40k samples. Concretely, we enhance raw affective images via generative redrawing to establish high-fidelity ground truths, and synthesize input images with divergent emotions and paired precise instructions. Fine-tuning a baseline model on AIM-40k yields a 9.15% relative improvement in overall performance, demonstrating the effectiveness of our AIM-40k. Our data and related code will be made open soon.

This manuscript presents PoreDiT, a novel generative model designed for high-efficiency digital rock reconstruction at gigavoxel scales. Addressing the significant challenges in digital rock physics (DRP), particularly the trade-off between resolution and field-of-view (FOV), and the computational bottlenecks associated with traditional deep learning architectures, PoreDiT leverages a three-dimensional (3D) Swin Transformer to break through these limitations. By directly predicting the binary probability field of pore spaces instead of grayscale intensities, the model preserves key topological features critical for pore-scale fluid flow and transport simulations. This approach enhances computational efficiency, enabling the generation of ultra-large-scale ($1024^3$ voxels) digital rock samples on consumer-grade hardware. Furthermore, PoreDiT achieves physical fidelity comparable to previous state-of-the-art methods, including accurate porosity, pore-scale permeability, and Euler characteristics. The model's ability to scale efficiently opens new avenues for large-domain hydrodynamic simulations and provides practical solutions for researchers in pore-scale fluid mechanics, reservoir characterization, and carbon sequestration.

Rare events are central to the evolution of complex many-body systems, characterized as key transitional configurations on the free energy surface (FES). Conventional methods require adequate sampling of rare event transitions to obtain the FES, which is computationally very demanding. Here we introduce the variational free energy surface (VaFES), a dataset-free framework that directly models FESs using tractable-density generative models. Rare events can then be immediately identified from the FES with their configurations generated directly via one-shot sampling of generative models. By extending a coarse-grained collective variable (CV) into its reversible equivalent, VaFES constructs a latent space of intermediate representation in which the CVs explicitly occupy a subset of dimensions. This latent-space construction preserves the physical interpretability and transparent controllability of the CVs by design, while accommodating arbitrary CV formulations. The reversibility makes the system energy exactly accessible, enabling variational optimization of the FES without pre-generated simulation data. A single optimization yields a continuous, differentiable FES together with one-shot generation of rare-event configurations. Our method can reproduce the exact analytical solution for the bistable dimer potential and identify a chignolin native folded state in close alignment with the experimental NMR structure. Our approach thus establishes a scalable, systematic framework for advancing the study of complex statistical systems.

The use of synthetic data in machine learning applications and research offers many benefits, including performance improvements through data augmentation and privacy preservation of original samples. This work proposes an efficient synthetic data generation method based on a fully connected neural network that transforms a high-dimensional random Gaussian distribution to approximate a target real-world dataset. The proposed solution combines data preprocessing designed for tabular data with distribution modeling and PCA dimensionality reduction to further enhance data privacy. The work also defines two dedicated randomized loss functions based on Wasserstein distance combined with feature Covariance and a randomized pairwise error reduction loss function. The experiments conducted on 25 diverse tabular real-world datasets confirm that the proposed solution obtains similarity and privacy scores relative to the state-of-the-art generative methods and achieves reference MMD scores orders of magnitude faster than modern deep learning solutions. The experiments involved analyzing distributional similarity, privacy protection, and the utility of synthetic data in classification tasks.

Modern financial systems generate vast quantities of transactional and event-level data that encode rich economic signals. This paper presents PRAGMA, a family of foundation models for banking event sequences. Our approach pre-trains a Transformer-based architecture with masked modelling on a large-scale, heterogeneous banking event corpus using a self-supervised objective tailored to the discrete, variable-length nature of financial records. The resulting model supports a wide range of downstream tasks such as credit scoring, fraud detection, and lifetime value prediction: strong performance can be achieved by training a simple linear model on top of the extracted embeddings and can be further improved with lightweight fine-tuning. Through extensive evaluation on downstream tasks, we demonstrate that PRAGMA achieves superior performance across multiple domains directly from raw event sequences, providing a general-purpose representation layer for financial applications.

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.

Graph-structured data jointly contain discrete topology and continuous geometry, which poses fundamental challenges for generative modeling due to heterogeneous distributions, incompatible noise dynamics, and the need for equivariant inductive biases. Existing flow-matching approaches for graph generation typically decouple structure from geometry, lack synchronized cross-domain dynamics, and rely on iterative sampling, often resulting in physically inconsistent molecular conformations and slow sampling. To address these limitations, we propose Equivariant MeanFlow (EQUIMF), a unified SE(3)-equivariant generative framework that jointly models discrete and continuous components through synchronized MeanFlow dynamics. EQUIMF introduces a unified time bridge and average-velocity updates with mutual conditioning between structure and geometry, enabling efficient few-step generation while preserving physical consistency. Moreover, we develop a novel discrete MeanFlow formulation with a simple yet effective parameterization to support efficient generation over discrete graph structures. Extensive experiments demonstrate that EQUIMF consistently outperforms prior diffusion and flow-matching methods in generation quality, physical validity, and sampling efficiency.

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.

Drifting models have recently gained attention for generating high-quality samples in a single forward pass. During training, they learn a push-forward map by following a vector-valued field, the drift field. We ask whether this procedure is equivalent to optimizing a scalar loss and find that, in general, it is not: drift fields are not conservative and cannot be written as the gradient of any scalar potential. We identify the position-dependent normalization as the source of non-conservatism, with the Gaussian kernel as the unique radial exception. Guided by this, we introduce the sharp kernel $k^\#$ and a sharp-normalized drift field that is conservative for general radial kernels. The resulting vector field is the gradient of a scalar potential that can be optimized directly using stochastic gradient descent. Moreover, the field has the form of a score difference of kernel density estimates, and gives exact equilibrium identifiability. Thus, sharp normalization closes the gap to related literature, such as Wasserstein gradient-flows and denoising score matching, also for non-Gaussian kernels. Empirically, sharp normalization preserves the performance of the original drifting objective, suggesting that the non-conservative flexibility is not required for high-quality generation.

Generating procedural synthetic data for multi-view stereo (MVS) usually requires writing complex rules to match the realism of curated datasets. We demonstrate that we can generate effective training data using SimpleProc: a new, fully procedural generator driven by a very small set of rules based on Non-Uniform Rational Basis Splines (NURBS), as well as simple displacement and texture patterns. At a modest scale of 8,000 images, our approach achieves superior results compared to manually curated images at the same scale sourced from games and real-world objects. When scaled to 352,000 images, our approach achieves similar, and in some benchmarks, even better results than the current state-of-the-art trained on over 692,000 manually curated images. The source code and the data are available at https://github.com/princeton-vl/SimpleProc.

The prevalence of missing values in data science poses a substantial risk to any further analyses. Despite a wealth of research, principled nonparametric methods to deal with general non-monotone missingness are still scarce. Instead, ad-hoc imputation methods are often used, for which it remains unclear whether the correct distribution can be recovered. In this paper, we propose FLOWGEM, a principled iterative method for generating a complete dataset from a dataset with values Missing at Random (MAR). Motivated by convergence results of the ignoring maximum likelihood estimator, our approach minimizes the expected Kullback-Leibler (KL) divergence between the observed data distribution and the distribution of the generated sample over different missingness patterns. To minimize the KL divergence, we employ a discretized particle evolution of the corresponding Wasserstein Gradient Flow, where the velocity field is approximated using a local linear estimator of the density ratio. This construction yields a data generation scheme that iteratively transports an initial particle ensemble toward the target distribution. Simulation studies and real-data benchmarks demonstrate that FLOWGEM achieves state-of-the-art performance across a range of settings, including the challenging case of non-monotone MAR mechanisms. Together, these results position FLOWGEM as a principled and practical alternative to existing imputation methods, and a decisive step towards closing the gap between theoretical rigor and empirical performance.

Flow Matching is typically built from Gaussian sources and Euclidean probability paths. For heavy-tailed or anisotropic data, however, a Gaussian source induces a structural mismatch already at the level of the radial distribution. We introduce Radial--Angular Flow Matching (RAFM), a framework that explicitly corrects this source mismatch within the standard simulation-free Flow Matching template. RAFM uses a source whose radial law matches that of the data and whose conditional angular distribution is uniform on the sphere, thereby removing the Gaussian radial mismatch by construction. This reduces the remaining transport problem to angular alignment, which leads naturally to conditional paths on scaled spheres defined by spherical geodesic interpolation. The resulting framework yields explicit Flow Matching targets tailored to radial--angular transport without modifying the underlying deterministic training pipeline. We establish the exact density of the matched-radial source, prove a radial--angular KL decomposition that isolates the Gaussian radial penalty, characterize the induced target vector field, and derive a stability result linking Flow Matching error to generation error. We further analyze empirical estimation of the radial law, for which Wasserstein and CDF metrics provide natural guarantees. Empirically, RAFM substantially improves over standard Gaussian Flow Matching and remains competitive with recent non-Gaussian alternatives while preserving a lightweight deterministic training procedure. Overall, RAFM provides a principled source-and-path design for Flow Matching on heavy-tailed and extreme-event data.