Generative Modeling

We design a new unconstrained coordinate system where a $p\times p$ symmetric positive definite (SPD) matrix $Θ$ is represented by a reverse telescoping map $Θ(x)=\rm{RT}(x)$, with $x=(v,d,r)\in\mathbb{R}\times\mathbb{R}^{(p-1)}\times\mathbb{R}^{p(p-1)/2}$, representing respectively the log volume or log determinant; and the shape, as encoded by log relative diagonal scales and partial covariances among the nodes. This construction results in important properties not available in other charts, e.g., matrix logarithm, such as Jacobian depending on only the log-determinant. A useful feature of our construction is $x$ contains a lossless symbolic representation of both the matrix and its inverse. Many important computations involving a matrix and its inverse can be performed in $O(p^2)$ in the transformed domain, while it is the rendering of results in matrix forms (on demand) that must incur an $O(p^3)$ cost. Moreover, two unit-determinant matrices in the transformed domain can be joined by a straight line with pathwise unit determinant. For generative modeling, this allows designing a split volume-shape flow model trained by conditional flow matching for transporting the shape over the unit-determinant path, with a separate one-dimensional flow for transporting the volume or the determinant. The forbidding SPD constraint, tamed thus into a powerful guiding force, leads to the surprising insight that it is in some sense easier to design a volume-normalized shape flow for SPD compared to the unconstrained $\mathbb{R}^{p\times p}$, with no intrinsic notion of volume to aid normalization, unlike the determinant of SPD matrices. We apply our construction for up to $p=200$ in generative modeling of SPD matrices on a difficult synthetic bimodal target, and in generating brain connectivity networks by models trained on fMRI data; as well as in intrinsic diffusion on the SPD manifold.

The fundamental limitation of traditional strand-based modeling is not simply data scarcity, but the ill-posedness of inferring complex 3D fields from 2D imagery without structural constraints. This unconstrained regression leads to catastrophic failures in resolving both global occlusion (e.g., in ponytails) and local directionality (e.g., in curls), resulting in over-smoothed, plausible-but-incorrect geometries. To resolve this, we integrate the strong geometric priors of Large Reconstruction Models (LRMs) into the strand generation pipeline. Using the LRM mesh as a structural anchor, we employ a novel Dual Orientation AutoEncoder to lift coarse geometry into high-fidelity strands. By resolving vector field singularities through latent-space optimization and surface-guided refinement, our method effectively disentangles complex topological structures, setting a new benchmark for robustness and accuracy in hair reconstruction.

Recursive training of generative models on their own outputs can lead to model collapse, a compounding drift away from the true data distribution. Existing theoretical works bound finite-round error accumulation in the context of diffusion models, but two questions remain open:~what distribution does the recursion converge to, and how fast? We answer both, isolating a mechanism distinct from imperfect learning: even with perfect score estimation and exact sampling, the early stopping of the reverse diffusion (required for numerical stability) drives a progressive drift away from the data distribution. We prove that this recursion converges geometrically to a unique limiting distribution, which admits a closed-form characterization as an infinite mixture of increasingly Gaussian-smoothed versions of the data distribution. A Hermite spectral decomposition of this limit reveals that recursive training acts as a low-pass filter: higher-order modes, which encode fine non-Gaussian structure, are attenuated much more strongly than coarse modes. This spectral picture motivates annealed truncation schedules that progressively shrink truncation times across retraining rounds; we prove that any schedule converging to $0$ asymptotically eliminates recursive compounding. Finally, we show our idealized characterization is robust: in the presence of discretization and score estimation errors, the learned distribution remains in a Wasserstein-2 ball around the ideal limit, with mode-dependent contraction rates that contract high-order errors faster than low-order ones. We validate the theory on synthetic Gaussian mixtures and CIFAR-10.

While flow-based generative models have demonstrated strong performance across a wide range of domains, deploying them in safety-critical physical systems remains challenging due to strict constraint requirements. Existing approaches typically enforce safety through post-hoc corrections, which incur substantial computational overhead and may distort the learned distribution. We propose PolyFlow, a polytope-constrained flow matching framework that embeds constraints directly into the model and flow dynamics. PolyFlow introduces a discrete-time flow formulation and a projection-free architecture, which eliminate the discretization error and guarantee strict satisfaction of arbitrary polyhedral constraints, without the need for expensive iterative solvers. Experimental results show that PolyFlow achieves zero constraint violation while maintaining high distributional fidelity across a range of planning and control tasks. Compared to state-of-the-art constrained generation baselines, PolyFlow significantly reduces inference latency and demonstrates a favorable trade-off between safety, efficiency, and generative quality. Code is available on https://github.com/MJianM/PolyFlow.

Continuous-state generative samplers, including diffusion and flow-matching models, evolve through continuous reverse-time dynamics, yet their samples often undergo abrupt qualitative changes: trajectories commit to modes, semantic alternatives collapse, and small perturbations in narrow time windows can produce large downstream effects. This paper develops a geometric account of such phase-transition-like behaviour. We view denoising as gradient descent on a free energy landscape and show that sharp transitions arise near projection caustics, where the nearest-point projection onto the data support ceases to be unique. Motivated by this perspective, we introduce the Critical Boundary Detector (CBD), as practical diagnostics for score-direction instability. Across toy models, standard diffusion models, and latent text-to-image diffusion models, CBD localises mode commitment, predicts intervention-sensitive windows, and supports targeted control in geometrically sensitive regions. Our results connect geometry of data and dynamics of diffusion generation.

We introduce a theoretical framework for analyzing federated learning in a generative setting through a teacher-multiple interacting students scenario, in which each student receives a distinct realization of the data, either through a different noise corruption or by accessing a different subset, possibly of varying size. Using theoretical tools in equilibrium disordered system, we analytically show that interactions among students systematically enhance learning performance: highly noisy students require fewer samples to recover the underlying pattern, while low-noise students achieve a larger overlap with the ground-truth signal. We derive the optimal Bayesian conditions for teacher recovery as functions of the sample complexity, noise level, and interaction strength, and validate these predictions through numerical simulations. The resulting dynamics can be mapped onto equilibrium sampling in a Restricted Boltzmann Machine with a structured hidden layer, providing a principled theoretical understanding of how interactions improve distributed generative modeling.

Two dominant approaches have emerged for generating probabilistic forecasts of physical systems: generative models, such as diffusion or flow matching; and ensembles of deterministic models with stochasticity injected, trained using the continuous ranked probability score (CRPS) loss. While both approaches have demonstrated strong predictive accuracy, the reliability of their uncertainties has not been systematically assessed. We address this gap by developing a framework to evaluate both approaches across diverse 2D spatiotemporal physical systems, under matched model size and computational budget. We assess the reliability of probabilistic emulation by inspecting the empirical coverage of predictive intervals, while also considering accuracy and computational efficiency metrics. CRPS-trained ensembles typically achieve more reliable uncertainties on both single-step prediction and autoregressive rollouts, demonstrating better coverage than the standard alternative of training generative models in a latent space. Moreover, the CRPS approach offers significantly faster inference. When generative models are trained in ambient rather than a compressed latent space, which is often infeasible for high-dimensional problems, they exhibit comparable coverage to CRPS-trained ensembles, though with substantially larger inference latency. In contrast, when CRPS-trained ensembles are trained in latent space they do not show a marked degradation in coverage with respect to ambient space. Both generative models and CRPS-trained ensembles demonstrate good predictive accuracy. To facilitate future research and application, we release AutoCast, a modular framework implementing both generative models and CRPS-trained ensembles, alongside AutoSim, a flexible dataset generation package for rapid prototyping.

Part-aware 3D generation aims to synthesize structured objects with semantically meaningful components, yet often suffers from structural ambiguity due to identity-layout entanglement. Existing methods either infer part identity and spatial layout implicitly, which can lead to unstable part allocation (e.g., slot swapping or part merging), or rely on strong layout conditions that are difficult to obtain in practice. We attribute this ambiguity to identity-slot permutation freedom: without explicit identity-slot alignment, the correspondence between semantic parts and generation slots is not identifiable during training, allowing multiple slot assignments to fit the same supervision and leading to inconsistent decomposition. Based on this insight, we argue that stable part-aware generation requires identity-aligned one-to-one slot modelling. We therefore propose an identity-slot aligned framework, ISAP-3D, which anchors each part with semantic identity tokens and performs identity-conditioned one-to-one layout prediction, followed by layout-conditioned geometry synthesis. Structured local-global conditioning maintains identity alignment across semantic, spatial, and geometric stages. We also construct a part-level dataset with a unified semantic protocol to enable learnable and consistent identity-slot alignment. Extensive experiments demonstrate improved structural stability, controllability, and robustness over state-of-the-art part-aware generation baselines.

Learning the compositional nature of the physical world requires joint observation of interacting factors. However, because practical data is often decentralized, these factors are fragmented across isolated silos. Existing decentralized generative approaches focus only on modeling the union of siloed data, overlooking novel combinations implied by the collective whole. To bridge this gap, we introduce Decentralized Compositional Flow Matching (DCFM), a framework that enforces structural constraints across the global set of generative factors, without exchanging any raw data. DCFM enables novel combinations to emerge through peer interactions, even when no single data source can independently support the composition. Empirically, DCFM substantially outperforms federated learning and mixture-of-experts baselines across conditional image generation, robotic spatial planning, and medical attribute co-occurrence modeling.

Standard diffusion models typically use a single time-homogeneous Gaussian terminal distribution as the reference law for generation. While this choice is analytically convenient and empirically powerful, it provides little explicit structure for data concentrated near low-dimensional manifolds, where different regions of the data distribution may correspond to distinct local geometric or semantic factors. As a result, the reverse model must recover manifold-level structure almost entirely from an unstructured terminal reference distribution. We propose PTL-Diffusion, a proof-of-concept diffusion framework whose forward noising process converges to a nonconstant periodic family of Gaussian terminal laws rather than to a single invariant law. Unlike a phase-conditioned DDPM, where phase information only enters the denoising network while the forward process remains unchanged, PTL-Diffusion embeds phase structure directly into the forward noising dynamics. The proposed construction remains close to standard denoising diffusion models: for a periodically forced Ornstein--Uhlenbeck-type forward process, we derive closed-form forward marginals, the limiting periodic Gaussian terminal family, and explicit Gaussian reverse posteriors, enabling standard noise-prediction training. We also introduce an invariant-average regularization term coupling the phase-conditioned reverse dynamics through the averaged periodic reference law. Experiments on torus and cylinder point-cloud benchmarks and the Olivetti face dataset show that PTL-Diffusion improves manifold-level distributional matching over matched DDPM baselines, reducing phase-conditioned errors, feature-space covariance errors, and nearest-neighbour manifold distances. These results suggest structured terminal reference laws as a promising direction, while motivating more expressive phase constructions and larger-scale evaluations.

Diffusion models have demonstrated remarkable generative capabilities and have also emerged as powerful self-supervised representation learners, yet the connection between these two abilities remains less explored. Drawing inspiration from self-supervised learning (SSL), we introduce a framework for jointly evaluating the representation and generation capabilities of diffusion models. Specifically, we decompose features into invariant and residual components and derive the Invariant Contamination Ratio (ICR), a Fisher-based metric that quantifies how residual variation contaminates invariant signal in feature space. We use this framework to analyze both discriminative and generative behavior of diffusion models. On the representation side, we find that invariance peaks at intermediate noise levels, which also yield the best downstream classification performance. On the generative side, we study how training transitions from genuine generalization to memorization in data-limited regimes, and show that ICR serves as a sensitive training-time indicator of early learning: increasing residual energy along Fisher directions marks the onset of memorization, detectable from training features alone without external evaluators or held-out test sets. Overall, our results show that diffusion models can be monitored from a self-supervised perspective through the geometry of their learned representations.

High-Dimensional Low-Sample Size (HDLSS) tabular domains (e.g., omics) are characterized by $n \ll m$, where $n$ = number of samples, and $m$ = number of features. Such domains often exhibit strong local correlation groups, sparse cross-group dependencies, heavy-tailed non-Gaussian marginals, heteroscedastic noise, and structured missingness, making direct density learning in $\mathbb{R}^m$ ill-conditioned since $n \ll m$. We propose BSTabDiff, a block-subunit generative framework that partitions the $m$ observed features into $M$ latent blocks ($M \ll m$) and generates each block via a shared low-dimensional subunit variable, concentrating global dependence learning in the compact block-latent space $\mathbb{R}^M$ while decoding to the full feature space with copula-driven dependence, flexible per-feature marginals, and explicit missingness mechanisms. BSTabDiff supports modern deep priors on block latents, including diffusion and normalizing flows, enabling stable synthesis and controllable benchmark generation in the HDLSS regime. Empirically, BSTabDiff produces more realistic and stable high-dimensional synthetic data when compared with unstructured tabular generators on HDLSS data.

Generative models are increasingly used to propose designs, data, and control actions for physical systems, yet many such systems are governed by hard physical constraints rather than by perceptual plausibility. Semiconductor manufacturing provides a demanding test case: generated masks, layouts, synthetic defect data, and process recipes must obey lithography, transport, reaction, and device-physics constraints, because physically invalid samples are not merely low quality but unusable. This Perspective argues that semiconductor manufacturing exposes a broader computational-science challenge, namely that generative AI for constrained physical domains must be physics-informed by construction, not corrected only through post-hoc filtering. We survey the emerging architectural toolkit, including physics-informed diffusion, PDE-constrained variational models, neural-operator priors, and conservation-law-respecting generative networks, and show how it connects to differentiable lithography, TCAD, process simulation, and autonomous experimentation. We identify four integration patterns between generative models and physics-based simulators, and we propose a research agenda centered on physics-fidelity benchmarks, differentiable simulator infrastructure, and multimodal foundation models for physical design and manufacturing. The central claim is analytical rather than rhetorical: where physical validity is the binding criterion of success, architectures that enforce it by construction should be expected to outperform those that filter for it after the fact, and the fab is the setting where this distinction is sharpest.

Standard flow and diffusion pre-training matches the distribution of available data (e.g., molecules), which often covers only a small fraction of the valid design space. In generative discovery, however, one aims to sample valid new-to-nature designs, assigned negligible probability under, and thus inaccessible to, standard models fitted to the observed data. To overcome this limitation, we depart from data distribution matching and view a generative model through its generable set: the region it covers with non-negligible probability. This allows to introduce a new learning principle for out-of-distribution flow modeling: enlarging a model's generable set to increase coverage of the valid design space. We propose Active Flow Expansion (ActFlow), a continued pre-training method that employs verifier feedback to expand a pre-trained model over new valid regions by iteratively adapting to synthetic data generated through active exploration in the learned flow representation. Theoretically, we establish to our knowledge first-of-their-kind statistical learning guarantees for out-of-distribution flow modeling, analyzing generable set expansion as a local-to-global reachability process over a learned representation. Empirically, we assess ActFlow with suitable out-of-distribution generative modeling metrics across small organic molecules, mid-sized drug-like molecules, therapeutic peptides, and protein sequence design tasks. Results show that ActFlow expands valid coverage far beyond the region modeled by the initial pre-trained model, significantly outperforming widely adopted synthetic flow pre-training methods.

Large and demographically balanced datasets are essential for reliable neuroimaging biomarkers. Full-resolution 3D brain MRI synthesis can support data augmentation in this setting, but existing approaches either incur prohibitive computational cost at volumetric scale or rely on lossy latent compression that may compromise anatomical detail. As a result, practical 3D generative augmentation often requires specialized compute infrastructure. We propose WaveDiT, a conditional flow matching framework operating in the coefficient space of a 3D Haar Discrete Wavelet Transform. The model combines factorized spatio-depth attention with band-wise heteroscedastic uncertainty modeling derived from higher-order wavelet statistics. Predicted log-variance is integrated directly into both the flow objective and conditioning pathway, enabling adaptive precision consistent with the heavy-tailed and input-dependent variance structure of anatomical detail. This formulation supports full-resolution 3D synthesis under practical memory and time constraints on a single modern GPU. Evaluation on a multi-site cohort demonstrates improved alignment between generated and real MRI distributions, together with enhanced downstream brain age prediction and region-level anatomical agreement relative to diffusion, latent, and wavelet-based baselines. Code is available at https://github.com/sisinflab/WaveDiT

This paper provides a theoretical account of memorization in stochastic interpolation models. By leveraging closed-form expressions for the optimal velocity field and the associated score function, we show that, in the continuous-time oracle setting, both deterministic and stochastic generation processes recover training samples. Under Euler discretization, generated samples remain centered around training samples, with deviations controlled by the step size. We further analyze generation in the presence of estimation errors and show that accumulated estimation errors control the endpoint deviation from the training set. These results imply that the generated sample admits a representation as a training sample perturbed by three controlled terms: a discretization-induced bound, an estimation-error-induced bound, and stochastic Gaussian noise. Based on this characterization, we provide theoretical definitions of overfitting and underfitting in generative models. Synthetic simulations support our theoretical findings.

Understanding what generative models retain from training data remains challenging, with implications for copyright and privacy. Beyond verbatim reproduction, models can encode subtler traces of their training data that never surface in their outputs yet remain exploitable. We study this regime for Rectified Flows, which are increasingly used in deployed generative systems. We analyse the interpolation path $X_λ= (1-λ)X_0 + λX_1$ that defines the Rectified Flow training. We show that a gap exists between the reconstruction of train and test data that follows a bell-shaped curve over $λ$, wich accumulates during training, while the validation metrics remain stable. The signal has a maximum whose location we derive in closed form under Gaussian assumptions. We validate these predictions on both audio and images and show that the bell-shaped structure is universal, while the peak prediction holds when our assumptions are satisfied. As a proof of concept, we exploit this specific $λ$-resolved structure to perform a Membership Inference Attack, distinguishing members of the training set from non-members.

While generative AI models have demonstrated remarkable success in structure-based drug design, they predominantly rely on deep binding pockets and struggle to sample effective ligands for challenging low-pocketability targets, such as the historically "undruggable" oncology targets KRAS and MYC. To address this gap, we introduce ShallowBench, a strictly curated benchmark of 5,780 shallow-pocket targets extracted from CrossDocked2020. By computing the difference between an Alpha Shape "lid" volume and the underlying protein atom voxel volume, we successfully isolated targets with low concavity while ensuring sufficient surface area for binding. Evaluating various state-of-the-art generative models reveals weaker predicted binding affinity on these low-concavity interfaces. ShallowBench therefore provides a rigorous benchmark for generative biology models and highlights the necessity of new architectural innovations or loss functions capable of navigating these challenging targets.

Safety-critical traffic scenario generation is essential for evaluating autonomous driving systems under rare but high-risk interactions. Existing diffusion-based methods offer strong controllability in closed-loop generation, but their iterative denoising process is computationally expensive and may accumulate sampling and guidance errors over long rollouts, causing unrealistic motion artifacts such as jitter, abnormal acceleration, and off-road behavior. To address these issues, we propose RiskFlow, a closed-loop safety-critical multi-agent traffic generation framework that formulates future trajectory generation as transport in the action space. Instead of relying on iterative denoising, RiskFlow learns an average velocity field over a finite interval to transform Gaussian action sequences into future acceleration and yaw-rate commands with a single forward pass, using a JVP-based objective for efficient and stable training. At test time, RiskFlow applies output-space guidance to the generated actions, steering selected critical agents toward risky interactions while regularizing off-road behavior, and reconstructs physically feasible trajectories through vehicle dynamics. Experiments on nuScenes with tbsim closed-loop evaluation show that RiskFlow achieves a strong adversariality-realism trade-off across multi-agent and long-horizon settings. Compared with representative baselines, RiskFlow consistently improves realism while maintaining competitive safety-critical generation capability, and substantially reduces inference time for evaluation.

Neurodegenerative disorders such as Alzheimer's disease exhibit highly organized patterns of regional brain vulnerability, yet the biological mechanisms underlying this spatial selectivity remain incompletely understood. Existing imaging-transcriptomic studies have largely relied on correlation-based analyses between gene expression and neuroimaging phenotypes, limiting their ability to model how molecular organization gives rise to neurodegeneration. Here, we introduce a cross-scale spatially-aware generative framework for modeling transcriptomic programs underlying cortical neurodegeneration. Regional transcriptomic profiles were derived from the Allen Human Brain Atlas using 910 landmark genes across 68 cortical regions. Neurodegenerative vulnerability maps were constructed from ADNI FreeSurfer cortical thickness measurements by computing regional cortical thinning differences between cognitively normal controls (NC = 926) and Alzheimer's disease subjects (AD = 426). A variational generative architecture was used to learn latent biological programs linking regional gene-expression organization to cortical degeneration while incorporating graph-based spatial smoothness regularization to preserve cortical organization. The proposed framework achieved strong prediction of regional neurodegenerative vulnerability, yielding an explained variance of 0.8604 and a significant spatial correlation between predicted and observed cortical degeneration profiles (r = 0.9439, p < 0.001). The learned latent representations revealed structured transcriptomic organization associated with distributed disease susceptibility. These findings demonstrate that biologically constrained generative modeling can bridge microscale molecular organization with macroscale neurodegeneration, providing a foundation for spatially-aware generative neurobiology and computational neuroscience.

Scenario generation is a critical component in stochastic programming (SP), as it directly influences the quality of decision-making under uncertainty. Existing approaches predominantly rely on either sampling-based techniques or supervised learning using neural networks. Sampling-based techniques often struggle to capture complex dependencies and rare but plausible events, while supervised learning requires fixed input-output pairs for training and is limited in its ability to generate a wide variety of realistic scenarios that are not restricted by predefined patterns or rules. To address these limitations, we introduce Diff2SP, a diffusion-based generative framework that incorporates downstream optimization objectives directly into scenario generation. Unlike conventional methods that treat scenario generation and decision-making as separate steps, Diff2SP embeds stochastic optimization into the training process, enabling the generation of scenarios that are both statistically coherent and decision-aware. To formally justify this optimization-aware design, we establish a regret bounds that link distributional accuracy to decision quality, and establish sample complexity guarantees showing faster convergence than traditional generative models such as GANs. Empirical results on both synthetic and power-system datasets validate these theoretical insights, demonstrating that Diff2SP consistently improves both statistical fidelity and downstream optimization outcomes.

Generating realistic and diverse graphs is a key problem in machine learning, with applications in molecular discovery, circuit design, cybersecurity, and beyond. However, current graph generative models remain limited by scalability and novelty. Diffusion-based methods often require costly full-adjacency operations and long denoising chains, while many autoregressive and hybrid models have at least quadratic complexity. In addition, these models often imitate training graphs rather than generalize beyond them. We propose a lightweight autoregressive framework to address these issues. It uses a structure-guided topological ordering to serialize graphs into regular edge sequences, enabling near log-linear generation, and a two-phase training strategy that combines exploration-oriented augmentation with iterative refinement to reduce overfitting and promote controlled novelty. Experiments on molecular and non-molecular benchmarks show that our approach improves novelty while preserving high validity and uniqueness. The framework also supports both LSTM and Mamba-style causal sequence backbones, with large-memory accelerators enabling longer graph-sequence experiments beyond typical GPU limits.

Single-view 3D generative models have achieved impressive visual quality, yet they are not designed to satisfy structural or functional requirements, and in practice, often fall short. Symmetry is one such requirement: violations, even subtle ones, on symmetry can render a model physically unusable. We present SymTRELLIS, a method that enforces arbitrary finite point group symmetries (rotational, reflectional, and polyhedral) during the flow-based 3D generation of TRELLIS.2, without retraining the underlying VAE or flow model. Our key idea is to approximate the latent-space action of spatial transformations as a learned linear operator on voxel latents, implemented as a lightweight spatial-transform latent mapper trained on generic, non-symmetric 3D data. At generation time, we enforce symmetry by averaging predicted flow velocities across all symmetry-equivalent transformations at each ODE step, a process we call velocity symmetrization. The symmetry specification can be estimated automatically from an initial TRELLIS.2 generation or supplied by the user, enabling deliberate fold manipulation beyond what the input image suggests. On a curated benchmark of 266 strictly symmetric objects spanning 2- to 20-fold rotations and polyhedral symmetry groups, SymTRELLIS substantially reduces all symmetry error metrics compared to TRELLIS.2, Hunyuan3D-2.1, and TripoSG, while maintaining reconstruction accuracy comparable to the base model.

Modern protein representation models support tasks such as enzyme design and drug discovery, but their reliance on static data such as sequence and native structure limits their ability to capture the conformational dynamics that drive protein function. We investigate whether persistent homology (PH) can provide descriptors shared across diverse proteins that retain global structure, fine-grained conformational variability, and kinetically relevant information without large-scale pretraining. We introduce the masked Flood complex, i.e., an adaptation of a recently proposed simplicial complex construction, that incorporates domain knowledge to emphasize inter-residue structure at low computational cost. We then use it to compute PH on molecular dynamics (MD) sampled structures, vectorize the persistence diagrams into a shared coordinate system, and probe the capacity of these representations in terms of the aforementioned aspects. To assess the amount of kinetic information, we learn low-dimensional embeddings from time-lagged observations and evaluate Markov state models (MSMs) estimated from them. Using these MSMs to guide training of the recent marsfm generative framework improves several ensemble statistics relative to the original model. After finetuning on lower-temperature MD data and adapting the sampling procedure, the resulting model also shows promising transfer to fast folding proteins.

We present PHAF-Personalized Hand Avatars in a Flash, a personalized photo-realistic hand avatar which provides high quality multi-view renders from just two images (dorsal and palmar views).Unlike slow optimization-based techniques, PHAF generates fast personalized textures for real-time deployment on edge devices. Our approach combines semantic guided mesh alignment and densified texture extraction to transfer high-frequency details efficiently. A view-based inpainting network refines textures ensuring smooth, continuous appearance. PHAF generalizes to novel viewpoints and leverages a parametric hand model for accurate articulations, making it compatible with standard graphics engines. Experiments show it is comparable to existing methods in visual fidelity while drastically reducing texture generation time by 30 times, enabling practical AR/VR applications.

Emerging distributed computing paradigms, such as the computing continuum, are inherently heterogeneous, stochastic, and complex. Efficiently and effectively utilizing all available resources across the continuum demands a unified formal model of the system. To address this gap, we propose a general framework for modeling distributed computing systems as a generative Markov model, factorized over a structured system state. In our model, the state decomposes into high-dimensional variables, each further factorized over its elements, reflecting the sparse dependency structure inherent to distributed systems. This yields a tractable model enabling simulation, inference, and policy learning over otherwise intractable system states, bridging distributed computing with Markov chain theory and reinforcement learning (RL). We demonstrate our framework through a case study of collaborative AI inference, in which a dedicated server combines resources with those volunteered by service users. Our results show that centralized scheduling becomes a bottleneck at scale, while distributing computation across user devices reduces both latency and server resource consumption. These findings highlight the value of adaptive decision-making in distributed computing systems and demonstrate the framework's utility for modeling, simulation, and optimization.

Constructing faithful 4D worlds from LiDAR-acquired sequences is crucial for embodied AI, yet current generative frameworks apply uniform modeling capacity across all spatial regions. This ignores that perceptual difficulty varies dramatically within a single scan: distant surfaces, occluded boundaries, and small-scale objects carry far higher uncertainty than well-observed structures. We present U4D, a new framework that explicitly leverages spatial uncertainty to guide LiDAR scene generation in a "hard-to-easy" schedule. U4D derives per-point uncertainty maps via Shannon Entropy from a pretrained segmentor, then applies an unconditional diffusion stage to synthesize high-entropy areas with precise geometry, followed by a conditional completion stage that fills in the remaining regions using these structures as priors. A MoST (Mixture of Spatio-Temporal) block further maintains cross-frame coherence by dynamically balancing spatial detail and temporal continuity. Extensive experiments on nuScenes and SemanticKITTI demonstrate state-of-the-art scene fidelity, temporal consistency, and downstream performance.

Urban trajectory generation is a fundamental task for transportation simulation, urban planning, and mobility analytics. However, systematic comparison across trajectory generation methods remains difficult because existing studies often rely on different datasets, preprocessing pipelines, trajectory representations, and evaluation metrics. This fragmentation makes it unclear whether reported performance differences arise from the generation mechanism itself or from inconsistent experimental protocols. To address this issue, we present CityTrajBench, a unified benchmark framework and protocol for city-scale vehicle trajectory generation. CityTrajBench standardizes data ingestion, trajectory normalization, feature construction, model adaptation, map-aware post-processing, model selection, and multi-level evaluation under a common setting. It supports heterogeneous generators, including statistical baselines, VAE-based, GAN-based, diffusion-based, and flow-matching-based models, and evaluates them on three real-world urban trajectory datasets. The benchmark measures global spatial realism, trip-level distribution fidelity, trajectory-level geometric similarity, conditional mobility consistency, and efficiency. Experiments reveal clear trade-offs across model families: DiffTraj is strongest on trajectory-level geometric fidelity, DiffRNTraj is competitive on structure-sensitive global realism, and TrajFlow provides a strong balance across realism, quality, conditional consistency, and efficiency. Meanwhile, a simple Markov baseline remains competitive on coarse-grained trip and local-movement statistics. These findings show that urban trajectory generation quality is inherently multi-objective, that no single model dominates all criteria equally, and that CityTrajBench provides a reproducible benchmark protocol and testbed for future research on urban mobility generation.

This study investigates the trade-offs between fidelity, privacy, and utility in synthetic data generation under conditions of data scarcity and privacy sensitivity. We propose an evaluation framework that jointly assesses these three dimensions and apply it to three widely used generative models, VAE, GAN, and DDPM. The evaluation spans three image datasets, MNIST, OCTMNIST, and OrganAMNIST, encompassing both general-purpose and medical imaging domains. Notable differences arise between the three models in their behaviour when differential privacy mechanisms are introduced during training. GAN and DDPM demonstrate greater robustness, maintaining higher fidelity and downstream utility across a range of noise levels, while VAE degrades more rapidly as privacy constraints increase. This study highlights the importance of a multidimensional evaluation of deep generative models, also noting that their behaviour significantly differs when privacy techniques are applied.

Diffusion models have emerged as a leading framework for deep generative modeling. While the standard Gaussian formulation is theoretically convenient, its suitability for heavy-tailed datasets remains unclear. To address this, heavy-tailed diffusion models (HTDMs) extend the standard formulation by replacing the Gaussian distribution with a Student's t-distribution, thereby improving tail fidelity on heavy-tailed datasets. Although stochastic differential equation (SDE)-based sampling is possible in HTDMs, it has not been fully explored. In this paper, we propose an SDE-based sampler for HTDMs that explicitly incorporates a state-dependent diffusion coefficient. This state dependence naturally induces a self-regulating annealing mechanism by adaptively modulating the effective noise scale. We theoretically explore this mechanism and experimentally verify its necessity for reproducing samples from a heavy-tailed distribution.