Physics-Informed Generative Modeling

Video generation models produce visually compelling results but systematically violate physical commonsense -- on VideoPhy-2, the best model achieves only 32.6% joint accuracy. We identify a specification bottleneck: text prompts are lossy compression of the physical world, omitting the parameters that fully determine dynamics, and no amount of model scaling can recover what was never specified. From this diagnosis we derive three properties that physics conditioning must satisfy -- sufficiency, dynamism, and verifiability -- and show that no existing approach satisfies all three. We present NEWTON, in which video generation is demoted from the system output to one action inside an agent's toolbox: a learned planner orchestrates physics-aware tools (keyframe generation, scientific computation, prompt refinement) to construct rich conditioning, and a verifier closes the loop for iterative re-planning. The planner is the sole trainable component, optimized on-policy via Flow-GRPO inside the live multi-turn loop. On VideoPhy-2, NEWTON improves joint accuracy from 21.4% to 29.7% on LTX-Video and from 30.7% to 37.4% on Veo-3.1, without modifying either generator. Our project page: https://Newton026.github.io/newton

Training and evaluating false data injection attack (FDIA) detectors for power systems is constrained by data scarcity. Operational grid measurements are commercially sensitive, and hand-crafted attacks fail to capture complex distributional structures imposed by network physics. We present GenAI-FDIA, a framework benchmarking a pool of $P{=}20$ architectures for physics-compliant FDIA synthesis, spanning Wasserstein GANs, MMD-VAEs, normalising flows, diffusion models, and cross-family hybrids. These are evaluated across three IEEE testbeds (14-bus DC, 30-bus DC, and 14-bus AC) under a 60/20/20 chronological split using data-driven Bad Data Detection (BDD) threshold calibration. Our empirical results verify that these models generate high-fidelity attacks, with all architectures achieving evasion rates of $ε_{\text{BDD}} \ge 86.6\%$ on the 14-bus network; additionally, limiting an attacker's topological knowledge induces a measurable degradation in stealthiness ($p \le 0.0022$). Crucially, we identify a previously unreported failure mode: applying affine physics projections directly in normalised feature spaces critically displaces the attack vector, collapsing BDD evasion from ${\sim}55\%$ to $<\!2\%$ on the 30-bus testbed. We resolve this via a novel inference-time harmoniser, restoring full stealthiness ($ε_{\text{BDD}}{=}100\%$) across all physics-informed variants without retraining. Finally, we isolate a covariance-collapse phenomenon ($κ\approx {-}0.076$) within advanced hybrid architectures and rectify it through 50-epoch warm-up schedules ($κ\to 0.785$, $Δ\text{MMD}={-}3.1\%$). Ultimately, GenAI-FDIA delivers a robust recovery blueprint applicable to any physics-constrained generative model deployed for power-system security.

Reconstructing PDE-governed fields from sparse and irregular measurements is challenging due to their ill-posed nature. Deterministic surrogates are trained on dense fields that struggle with limited measurements and uncertainty quantification. Generative models, by learning distributions over spatiotemporal fields, can better handle sparsity and uncertainty. However, existing generative approaches enforce data consistency and PDE constraints simultaneously via sampling-time gradient guidance, resulting in slow and unstable inference. To this end, we propose PerFlow, a Physics-embedded rectified Flow for efficient sparse reconstruction and uncertainty quantification of spatiotemporal dynamics. PerFlow decouples observation conditioning from physics enforcement, performing guidance-free conditioning by feeding observations into rectified-flow dynamics while embedding hard physics via a constraint-preserving projection (e.g., incompressibility or conservation). Theoretically, we establish invariance guarantees to ensure that trajectories remain on the physics-consistent manifold throughout sampling. Experiments on various PDE systems demonstrate competitive reconstruction accuracy with sound physics consistency, while enabling efficient conditional sampling (e.g., 50 steps) and up to 320x faster inference than 2000-step guided diffusion baselines.

Modern video diffusion models excel at appearance synthesis but still struggle with physical consistency: objects drift, collisions lack realistic rebound, and material responses seldom match their underlying properties. We present PhyCo, a framework that introduces continuous, interpretable, and physically grounded control into video generation. Our approach integrates three key components: (i) a large-scale dataset of over 100K photorealistic simulation videos where friction, restitution, deformation, and force are systematically varied across diverse scenarios; (ii) physics-supervised fine-tuning of a pretrained diffusion model using a ControlNet conditioned on pixel-aligned physical property maps; and (iii) VLM-guided reward optimization, where a fine-tuned vision-language model evaluates generated videos with targeted physics queries and provides differentiable feedback. This combination enables a generative model to produce physically consistent and controllable outputs through variations in physical attributes-without any simulator or geometry reconstruction at inference. On the Physics-IQ benchmark, PhyCo significantly improves physical realism over strong baselines, and human studies confirm clearer and more faithful control over physical attributes. Our results demonstrate a scalable path toward physically consistent, controllable generative video models that generalize beyond synthetic training environments.

Optical microrobots actuated by optical tweezers (OT) are important for cell manipulation and microscale assembly, but their autonomous operation depends on accurate 3D perception. Developing such perception systems is challenging because large-scale, high-quality microscopy datasets are scarce, owing to complex fabrication processes and labor-intensive annotation. Although generative AI offers a promising route for data augmentation, existing generative adversarial network (GAN)-based methods struggle to reproduce key optical characteristics, particularly depth-dependent diffraction and defocus effects. To address this limitation, we propose Du-FreqNet, a dual-control, frequency-aware diffusion model for physically consistent microscopy image synthesis. The framework features two independent ControlNet branches to encode microrobot 3D point clouds and depth-specific mesh layers, respectively. We introduce an adaptive frequency-domain loss that dynamically reweights high- and low-frequency components based on the distance to the focal plane. By leveraging differentiable FFT-based supervision, Du-FreqNet captures physically meaningful frequency distributions often missed by pixel-space methods. Trained on a limited dataset (e.g., 80 images per pose), our model achieves controllable, depth-dependent image synthesis, improving SSIM by 20.7% over baselines. Extensive experiments demonstrate that Du-FreqNet generalizes effectively to unseen poses and significantly enhances downstream tasks, including 3D pose and depth estimation, thereby facilitating robust closed-loop control in microrobotic systems.

Synthetic Aperture Radar (SAR) imagery generation is essential for deepening the study of scattering mechanisms, establishing trustworthy electromagnetic scene models, and fundamentally alleviating the data scarcity bottleneck that constrains development in this field. However, existing methods find it difficult to simultaneously ensure high fidelity in both global geospatial semantics and microscopic scattering mechanisms, resulting in severe challenges for global generation. To address this, we propose HuiYanEarth-SAR, the first foundational SAR imagery generation model based on AlphaEarth and integrated scattering mechanisms. By injecting geospatial priors to control macroscopic structures and utilizing implicit scattering characteristic modeling to ensure the authenticity of microscopic textures, we achieve the capability of generating high-fidelity SAR images for global locations solely based on geographic coordinates. This study not only constructs an efficient SAR scene simulator but also establishes a bridge connecting geography, scatter mechanism, and artificial intelligence from a methodological standpoint. It advances SAR research by expanding the paradigm from perception and understanding to simulation and creation, providing key technical support for constructing a high-confidence digital twin of the Earth.

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.

Existing methods for single-image 3D indoor scene generation often produce visually plausible results that violate real-world physical constraints, limiting their reliability in robotics, embodied AI, and virtual environment design. To bridge this gap, we introduce a Physics Evaluator that assesses four aspects (geometric priors, contact, stability, and deployability) through nine sub-constraints, establishing a benchmark for evaluating physical consistency. Our analysis reveals that even state-of-the-art methods produce scenes with substantial physical inconsistencies despite their visual plausibility. To address these limitations, we propose a framework that incorporates feedback from the Physics Evaluator into both training and inference to improve the physical plausibility of generated scenes. Specifically, PhyMix comprises two components: (i) implicit alignment via Scene-GRPO, a critic-free group-relative preference optimization strategy that uses physical evaluations to guide the generator toward physically plausible layouts, and (ii) explicit refinement via verifier-guided agentic repair, which translates evaluator diagnostics into executable scene-editing skills to correct residual violations at inference time. PhyMix unifies physical evaluation, preference-based alignment, and agentic inference-time correction to improve physical plausibility while retaining the observed scene content. Experiments show improvements in reconstruction quality and physical plausibility, while qualitative examples on stylized and real-world images illustrate the applicability of the framework beyond synthetic inputs.

Recent advances in generative video modeling, driven by large-scale datasets and powerful architectures, have yielded remarkable visual realism. However, emerging evidence suggests that simply scaling data and model size does not endow these systems with an understanding of the underlying physical laws that govern real-world dynamics. Existing approaches often fail to capture or enforce such physical consistency, resulting in unrealistic motion and dynamics. In his work, we investigate whether integrating the inference of latent physical properties directly into the video generation process can equip models with the ability to produce physically plausible videos. To this end, we propose Phantom, a Physics-Infused Video Generation model that jointly models the visual content and latent physical dynamics. Conditioned on observed video frames and inferred physical states, Phantom jointly predicts latent physical dynamics and generates future video frames. Phantom leverages a physics-aware video representation that serves as an abstract yet informaive embedding of the underlying physics, facilitating the joint prediction of physical dynamics alongside video content without requiring an explicit specification of a complex set of physical dynamics and properties. By integrating the inference of physical-aware video representation directly into the video generation process, Phantom produces video sequences that are both visually realistic and physically consistent. Quantitative and qualitative results on both standard video generation and physics-aware benchmarks demonstrate that Phantom not only outperforms existing methods in terms of adherence to physical dynamics but also delivers competitive perceptual fidelity.

Granular flows govern many natural and industrial processes, yet their interior kinematics and mechanics remain largely unobservable, as experiments access only boundaries or free surfaces. Conventional numerical simulations are computationally expensive for fast inverse reconstruction, and deterministic models tend to collapse to over-smoothed mean predictions in ill-posed settings. This study, to the best of the authors' knowledge, presents the first conditional flow matching (CFM) framework for granular-flow reconstruction from sparse boundary observations. Trained on high-fidelity particle-resolved discrete element simulations, the generative model is guided at inference by a differentiable forward operator and a novel sparsity-aware gradient guidance mechanism. This mechanism avoids the gradient dilution inherent to standard mean-squared-error approaches, preserves the absolute physical scale of observation errors, enforces measurement consistency without hyperparameter tuning, and prevents unphysical velocity predictions in non-material regions. A physics decoder maps the reconstructed velocity fields to stress states and energy fluctuation quantities, including mean stress, deviatoric stress, and granular temperature. The framework accurately recovers interior flow fields from full observation to only 16% of the informative window, and it remains effective under strongly diluted spatial resolution with only 11% of data. It also outperforms a deterministic CNN baseline in the most ill-posed reconstruction regime and provides spatially resolved uncertainty estimates through ensemble generation. These results demonstrate that conditional generative modeling offers a practical route for non-invasive inference of hidden bulk mechanics in granular media, and it suggests potential applicability for inverse problems in particulate and multiphase systems.

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.

Generative artificial intelligence offers a new paradigm to design matter in high-dimensional spaces. However, its underlying mechanisms remain difficult to interpret and limit adoption in computational mechanics. This gap is striking because its core tools-diffusion, stochastic differential equations, and inverse problems-are fundamental to the mechanics of materials. Here we show that diffusion-based generative AI and computational mechanics are rooted in the same principles. We illustrate this connection using a three-ingredient burger as a minimal benchmark for material design in a low-dimensional space, where both forward and reverse diffusion admit analytical solutions: Markov chains with Bayesian inversion in the discrete case and the Ornstein-Uhlenbeck process with score-based reversal in the continuous case. We extend this framework to a high-dimensional design space with 146 ingredients and 8.9x10^43 possible configurations, where analytical solutions become intractable. We therefore learn the discrete and continuous reverse processes using neural network models that infer inverse dynamics from data. We train the models on only 2,260 recipes and generate one million samples that capture the statistical structure of the data, including ingredient prevalence and quantitative composition. We further generate five new burgers and validate them in a blinded restaurant-based sensory study with n = 101 participants, where three of the AI-designed burgers outperform the classical Big Mac in overall liking, flavor, and texture. These results establish diffusion-based generative modeling as a physically grounded approach to design in high-dimensional spaces. They position generative AI as a natural extension of computational mechanics, with applications from burgers to matter, and establish a path toward data-driven, physics-informed generative design.

Despite advancements in generating visually stunning content, video diffusion models (VDMs) often yield physically inconsistent results due to pixel-only reconstruction. To address this, we propose MMPhysVideo, the first study to enhance physical plausibility in video generation through joint multimodal modeling. We recast perceptual cues, specifically semantics, geometry, and spatio-temporal trajectories, into a unified pseudo-RGB format, enabling VDMs to directly capture complex physical dynamics. To mitigate cross-modal interference, we propose a Bidirectionally Controlled Teacher architecture, which utilizes parallel branches to fully decouple RGB and perception processing and adopts two zero-initialized control links to gradually establish pixel-wise consistency. For inference efficiency, the teacher's physical prior is distilled into a single-stream student model via representation alignment. Furthermore, we present MMPhysPipe, an end-to-end data curation and annotation pipeline tailored for constructing physics-rich multimodal datasets. MMPhysPipe employs a vision-language model (VLM) guided by a chain-of-visual-evidence rule to pinpoint physical subjects, enabling expert models to extract multi-granular perceptual information. Without additional inference costs, MMPhysVideo consistently improves physical plausibility of advanced models on the Videophy and PhyGenbench benchmarks and achieves superior performance among existing methods.

The deployment of reinforcement learning (RL)-based controllers on physical systems is often limited by poor generalization to real-world scenarios, known as the simulation-to-reality (sim-to-real) gap. This gap is particularly challenging in spaceflight, where real-world training data are scarce due to high cost and limited planetary exploration data. Traditional approaches, such as system identification and synthetic data generation, depend on sufficient data and often fail due to modeling assumptions or lack of physics-based constraints. We propose addressing this data scarcity by introducing physics-based learning bias in a generative model. Specifically, we develop the Mutual Information-based Split Variational Autoencoder (MI-VAE), a physics-informed VAE that learns differences between observed system trajectories and those predicted by physics-based models. The latent space of the MI-VAE enables generation of synthetic datasets that respect physical constraints. We evaluate MI-VAE on a planetary lander problem, focusing on limited real-world data and offline RL training. Results show that augmenting datasets with MI-VAE samples significantly improves downstream RL performance, outperforming standard VAEs in statistical fidelity, sample diversity, and policy success rate. This work demonstrates a scalable strategy for enhancing autonomous controller robustness in complex, data-constrained environments.

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.

Accurate LiDAR simulation is crucial for autonomous driving, especially under adverse weather conditions. Existing methods struggle to capture the complex interactions between LiDAR signals and atmospheric phenomena, leading to unrealistic representations. This paper presents a physics-informed learning framework (PICWGAN) for generating realistic LiDAR data under adverse weather conditions. By integrating physicsdriven constraints for modeling signal attenuation and geometryconsistent degradations into a physics-informed learning pipeline, the proposed method reduces the sim-to-real gap. Evaluations on real-world datasets (CADC for snow, Boreas for rain) and the VoxelScape dataset show that our approach closely mimics realworld intensity patterns. Quantitative metrics, including MSE, SSIM, KL divergence, and Wasserstein distance, demonstrate statistically consistent intensity distributions. Additionally, models trained on data enhanced by our framework outperform baselines in downstream 3D object detection, achieving performance comparable to models trained on real-world data. These results highlight the effectiveness of the proposed approach in improving the realism of LiDAR data and enabling robust perception under adverse weather conditions.

Diffusion models have emerged as a powerful framework for generative tasks in deep learning. They decompose generative modeling into two computational primitives: deterministic neural-network evaluation and stochastic sampling. Current implementations usually place most computation in the neural network, but diffusion as a framework allows a broader range of choices for the stochastic transition kernel. Here, we generalize the stochastic sampling component by replacing independent noise injection with Markov chain Monte Carlo (MCMC) dynamics that incorporate known interaction structure. Standard independent diffusion is recovered as a special case when couplings are set to zero. By explicitly incorporating Ising couplings into the diffusion dynamics, the noising and denoising processes exploit spatial correlations representative of the target system. The resulting framework maps naturally onto probabilistic computers (p-computers) built from probabilistic bits (p-bits), which provide orders-of-magnitude advantages in sampling throughput and energy efficiency over GPUs. We demonstrate the approach on equilibrium states of the 2D ferromagnetic Ising model and the 3D Edwards-Anderson spin glass, showing that correlated diffusion produces samples in closer agreement with MCMC reference distributions than independent diffusion. More broadly, the framework shows that p-computers can enable new classes of diffusion algorithms that exploit structured probabilistic sampling for generative modeling.

Generative video models achieve high visual fidelity but often violate basic physical principles, limiting reliability in real-world settings. Prior attempts to inject physics rely on conditioning: frame-level signals are domain-specific and short-horizon, while global text prompts are coarse and noisy, missing fine-grained dynamics. We present PhysVid, a physics-aware local conditioning scheme that operates over temporally contiguous chunks of frames. Each chunk is annotated with physics-grounded descriptions of states, interactions, and constraints, which are fused with the global prompt via chunk-aware cross-attention during training. At inference, we introduce negative physics prompts (descriptions of locally relevant law violations) to steer generation away from implausible trajectories. On VideoPhy, PhysVid improves physical commonsense scores by $\approx 33\%$ over baseline video generators, and by up to $\approx 8\%$ on VideoPhy2. These results show that local, physics-aware guidance substantially increases physical plausibility in generative video and marks a step toward physics-grounded video models.

Flow-matching video generators produce temporally coherent, high-fidelity outputs yet routinely violate elementary physics because their reconstruction objectives penalize per-frame deviations without distinguishing physically consistent dynamics from impossible ones. Contrastive flow matching offers a principled remedy by pushing apart velocity-field trajectories of differing conditions, but we identify a fundamental obstacle in the text-conditioned video setting: semantic-physics entanglement. Because natural-language prompts couple scene content with physical behavior, naive negative sampling draws conditions whose velocity fields largely overlap with the positive sample's, causing the contrastive gradient to directly oppose the flow-matching objective. We formalize this gradient conflict, deriving a precise alignment condition that reveals when contrastive learning helps versus harms training. Guided by this analysis, we introduce DiReCT (Disentangled Regularization of Contrastive Trajectories), a lightweight post-training framework that decomposes the contrastive signal into two complementary scales: a macro-contrastive term that draws partition-exclusive negatives from semantically distant regions for interference-free global trajectory separation, and a micro-contrastive term that constructs hard negatives sharing full scene semantics with the positive sample but differing along a single, LLM-perturbed axis of physical behavior; spanning kinematics, forces, materials, interactions, and magnitudes. A velocity-space distributional regularizer helps to prevent catastrophic forgetting of pretrained visual quality. When applied to Wan 2.1-1.3B, our method improves the physical commonsense score on VideoPhy by 16.7% and 11.3% compared to the baseline and SFT, respectively, without increasing training time.

Learning-based models for fluid dynamics often operate in unconstrained function spaces, leading to physically inadmissible, unstable simulations. While penalty-based methods offer soft regularization, they provide no structural guarantees, resulting in spurious divergence and long-term collapse. In this work, we introduce a unified framework that enforces the incompressible continuity equation as a hard, intrinsic constraint for both deterministic and generative modeling. First, to project deterministic models onto the divergence-free subspace, we integrate a differentiable spectral Leray projection grounded in the Helmholtz-Hodge decomposition, which restricts the regression hypothesis space to physically admissible velocity fields. Second, to generate physically consistent distributions, we show that simply projecting model outputs is insufficient when the prior is incompatible. To address this, we construct a divergence-free Gaussian reference measure via a curl-based pushforward, ensuring the entire probability flow remains subspace-consistent by construction. Experiments on 2D Navier-Stokes equations demonstrate exact incompressibility up to discretization error and substantially improved stability and physical consistency.

Stochastic human motion prediction aims to generate diverse, plausible futures from observed sequences. Despite advances in generative modeling, existing methods often produce predictions corrupted by high-frequency jitter and temporal discontinuities. To address these challenges, we introduce KHMP, a novel framework featuring an adaptiveKalman filter applied in the DCT domain to generate high-fidelity human motion predictions. By treating high-frequency DCT coefficients as a frequency-indexed noisy signal, the Kalman filter recursively suppresses noise while preserving motion details. Notably, its noise parameters are dynamically adjusted based on estimated Signal-to-Noise Ratio (SNR), enabling aggressive denoising for jittery predictions and conservative filtering for clean motions. This refinement is complemented by training-time physical constraints (temporal smoothness and joint angle limits) that encode biomechanical principles into the generative model. Together, these innovations establish a new paradigm integrating adaptive signal processing with physics-informed learning. Experiments on the Human3.6M and HumanEva-I datasets demonstrate that KHMP achieves state-of-the-art accuracy, effectively mitigating jitter artifacts to produce smooth and physically plausible motions.

Data assimilation (DA) for systems governed by partial differential equations (PDE) aims to reconstruct full spatiotemporal fields from sparse high-fidelity (HF) observations while respecting physical constraints. While full-grid low-fidelity (LF) simulations provide informative priors in multi-fidelity settings, recovering an HF field consistent with both sparse observations and the governing PDE typically requires per-instance test-time optimization, which becomes a major bottleneck in time-critical applications. To alleviate this, amortized reconstruction using generative models has recently been proposed; however, such approaches rely on full-field HF supervision during training, which is often impractical in real-world settings. From a more realistic perspective, we propose the Physics-Informed Conditional Schrödinger Bridge (PICSB), which transports an informative LF prior toward an observation-conditioned HF posterior without any additional inference-time guidance. To enable learning without HF endpoints, PICSB employs an iterative surrogate-endpoint refresh scheme, and directly incorporates PDE residuals into the training objective while enforcing observations via hard conditioning throughout sampling. Experiments on fluid PDE benchmarks demonstrate that PICSB enables extremely fast spatiotemporal field reconstruction while maintaining competitive accuracy under sparse HF supervision.

Earthquake hazard analysis and design of spatially distributed infrastructure, such as power grids and energy pipeline networks, require scenario-specific ground-motion time histories with realistic frequency content and spatiotemporal coherence. However, producing the large ensembles needed for uncertainty quantification with physics-based simulations is computationally intensive and impractical for engineering workflows. To address this challenge, we introduce Ground-Motion Flow (GMFlow), a physics-inspired latent operator flow matching framework that generates realistic, large-scale regional ground-motion time-histories conditioned on physical parameters. Validated on simulated earthquake scenarios in the San Francisco Bay Area, GMFlow generates spatially coherent ground motion across more than 9 million grid points in seconds, achieving a 10,000-fold speedup over the simulation workflow, which opens a path toward rapid and uncertainty-aware hazard assessment for distributed infrastructure. More broadly, GMFlow advances mesh-agnostic functional generative modeling and could potentially be extended to the synthesis of large-scale spatiotemporal physical fields in diverse scientific domains.

Generalizing across disparate physical laws remains a fundamental challenge for artificial intelligence in science. Existing deep-learning solvers are largely confined to single-equation settings, limiting transfer across physical regimes and inference tasks. Here we introduce pADAM, a unified generative framework that learns a shared probabilistic prior across heterogeneous partial differential equation families. Through a learned joint distribution of system states and, where applicable, physical parameters, pADAM supports forward prediction and inverse inference within a single architecture without retraining. Across benchmarks ranging from scalar diffusion to nonlinear Navier--Stokes equations, pADAM achieves accurate inference even under sparse observations. Combined with conformal prediction, it also provides reliable uncertainty quantification with coverage guarantees. In addition, pADAM performs probabilistic model selection from only two sparse snapshots, identifying governing laws through its learned generative representation. These results highlight the potential of generative multi-physics modeling for unified and uncertainty-aware scientific inference.

Motivation: Generative models for protein backbone design have to simultaneously ensure geometric validity, sampling efficiency, and scalability to long sequences. However, most existing approaches rely on iterative refinement, quadratic attention mechanisms, or post-hoc geometry correction, leading to a persistent trade-off between computational efficiency and structural fidelity. Results: We present Physics-Informed Mamba (PI-Mamba), a generative model that enforces exact local covalent geometry by construction while enabling linear-time inference. PI-Mamba integrates a differentiable constraint-enforcement operator into a flow-matching framework and couples it with a Mamba-based state-space architecture. To improve optimisation stability and backbone realism, we introduce a spectral initialization derived from the Rouse polymer model and an auxiliary cis-proline awareness head. Across benchmark tasks, PI-Mamba achieves 0.0% local geometry violations and high designability (scTM = $0.91\pm 0.03$, n = 100), while scaling to proteins exceeding 2,000 residues on a single A5000 GPU (24 GB).

Denoising generative models have recently become the dominant paradigm for dexterous grasp generation, owing to their ability to model complex grasp distributions from large-scale data. However, existing diffusion-based methods typically formulate generation as a stochastic differential equation (SDE), which often requires many sequential denoising steps and introduces trajectory instability that can lead to physically infeasible grasps. In this paper, we propose EFF-Grasp, a novel Flow-Matching-based framework for physics-aware dexterous grasp generation. Specifically, we reformulate grasp synthesis as a deterministic ordinary differential equation (ODE) process, which enables efficient and stable generation through smooth probability flows. To further enforce physical feasibility, we introduce a training-free physics-aware energy guidance strategy. Our method defines an energy-guided target distribution using adapted explicit physical energy functions that capture key grasp constraints, and estimates the corresponding guidance term via a local Monte Carlo approximation during inference. In this way, EFF-Grasp dynamically steers the generation trajectory toward physically feasible regions without requiring additional physics-based training or simulation feedback. Extensive experiments on five benchmark datasets show that EFF-Grasp achieves superior performance in grasp quality and physical feasibility, while requiring substantially fewer sampling steps than diffusion-based baselines.

Objectives: Full-waveform inversion (FWI) is a high-resolution geophysical imaging technique that reconstructs subsurface velocity models by iteratively minimizing the misfit between predicted and observed seismic data. However, under complex geological conditions, conventional FWI suffers from strong dependence on the initial model and tends to produce unstable results when the data are sparse or contaminated by noise. Methods: To address these limitations, this paper proposes a physics-driven generative adversarial network-based full-waveform inversion method. The proposed approach integrates the data-driven capability of deep neural networks with the physical constraints imposed by the seismic wave equation, and employs adversarial training through a discriminator to enhance the stability and robustness of the inversion results. Results: Experimental results on two representative benchmark geological models demonstrate that the proposed method can effectively recover complex velocity structures and achieves superior performance in terms of structural similarity (SSIM) and signal-to-noise ratio (SNR). Conclusions: This method provides a promising solution for alleviating the initial-model dependence in full-waveform inversion and shows strong potential for practical applications.

This study presents a conditional flow matching framework for solving physics-constrained Bayesian inverse problems. In this setting, samples from the joint distribution of inferred variables and measurements are assumed available, while explicit evaluation of the prior and likelihood densities is not required. We derive a simple and self-contained formulation of both the unconditional and conditional flow matching algorithms, tailored specifically to inverse problems. In the conditional setting, a neural network is trained to learn the velocity field of a probability flow ordinary differential equation that transports samples from a chosen source distribution directly to the posterior distribution conditioned on observed measurements. This black-box formulation accommodates nonlinear, high-dimensional, and potentially non-differentiable forward models without restrictive assumptions on the noise model. We further analyze the behavior of the learned velocity field in the regime of finite training data. Under mild architectural assumptions, we show that overtraining can induce degenerate behavior in the generated conditional distributions, including variance collapse and a phenomenon termed selective memorization, wherein generated samples concentrate around training data points associated with similar observations. A simplified theoretical analysis explains this behavior, and numerical experiments confirm it in practice. We demonstrate that standard early-stopping criteria based on monitoring test loss effectively mitigate such degeneracy. The proposed method is evaluated on several physics-based inverse problems. We investigate the impact of different choices of source distributions, including Gaussian and data-informed priors. Across these examples, conditional flow matching accurately captures complex, multimodal posterior distributions while maintaining computational efficiency.

Video Diffusion Models (VDMs) offer a promising approach for simulating dynamic scenes and environments, with broad applications in robotics and media generation. However, existing models often generate temporally incoherent content that violates basic physical intuition, significantly limiting their practical applicability. We propose PhysAlign, an efficient framework for physics-coherent image-to-video (I2V) generation that explicitly addresses this limitation. To overcome the critical scarcity of physics-annotated videos, we first construct a fully controllable synthetic data generation pipeline based on rigid-body simulation, yielding a highly-curated dataset with accurate, fine-grained physics and 3D annotations. Leveraging this data, PhysAlign constructs a unified physical latent space by coupling explicit 3D geometry constraints with a Gram-based spatio-temporal relational alignment that extracts kinematic priors from video foundation models. Extensive experiments demonstrate that PhysAlign significantly outperforms existing VDMs on tasks requiring complex physical reasoning and temporal stability, without compromising zero-shot visual quality. PhysAlign shows the potential to bridge the gap between raw visual synthesis and rigid-body kinematics, establishing a practical paradigm for genuinely physics-grounded video generation. The project page is available at https://physalign.github.io/PhysAlign.

Global numerical weather prediction (NWP) and artificial intelligence (AI) models often underestimate tropical cyclone (TC) intensity, partly because coarse grids underresolve fine-scale three-dimensional inner-core structures that influence TC intensity evolution. Kilometer-scale NWP simulations can better resolve these structures but are too costly for operational use, which also makes high-resolution TC data limited. Here we construct a 3-km, TC-centered dataset for 2018--2024 using the Weather Research and Forecasting (WRF) model and develop 3DTCR, a vortex-following generative framework that reconstructs three-dimensional TC structure from FuXi global forecasts. 3DTCR combines conditional flow matching (CFM) with two-stage training to learn a coarse-to-fine mapping from center-aligned reanalysis simulation pairs and then adapt it to forecast inputs through latent space alignment. Evaluated on 2024 western North Pacific (WNP) forecasts, 3DTCR reduces the root mean square error (RMSE) and the magnitude of the mean bias error (MBE) in maximum 10-m wind speed by 36.5% and 60.7% relative to FuXi, and by 8.9% and 28.2% relative to the European Centre for Medium-Range Weather Forecasts high-resolution system (ECMWF-HRES), respectively. Case studies suggest that reconstructions capture wind gradients between the eye and eyewall, vertical structure of horizontal winds, and vortex asymmetries, while inheriting the FuXi-predicted TC tracks. 3DTCR generates 5-day TC-centered atmospheric fields in approximately 3 minutes on one GPU, whereas a full-basin 3-km WRF simulation takes about 400 hours on 32 CPU cores. These results demonstrate that such a vortex-following generative reconstruction can add localized three-dimensional detail to global forecasts and improve TC intensity prediction without basin-wide kilometer-scale numerical integration.