Physics-Informed Generative Modeling

Recent methods have made promising progress in generating interactions between two humanoids, largely relying on physics-based tracking policies to convert digital reference motions into executable trajectories. However, limited tracking capabilities restrict the range of reference motions that can be successfully executed, reducing data utilization. Moreover, even successful tracking does not guarantee physically plausible responses or faithful realization of the intended interactions. In this paper, we introduce DIGHT, a co-adaptive framework that couples a Digital human Interaction Generator with a Humanoid Tracking policy. Our DIGHT first executes multiple text-conditioned interaction candidates in simulation using a fixed tracker. It then constructs physics-grounded preferences from the resulting rollouts, covering both general executability and interaction fidelity. Rather than collapsing these signals into a single scalar reward for candidate ranking, we align the pretrained generator using physics-decoupled diffusion direct preference optimization (DPO), preserving criterion-specific supervision without differentiating through the simulator. To improve executability, preference pairs are derived from tracking error, friction, and floating. Additionally, to improve interaction fidelity, we propose to incorporate force feedback from simulator as a measure of contact fidelity and construct preferences over contact occurrence, location, duration, and force magnitude. The aligned generator then supplies reference motions for fine-tuning the tracker, improving compatibility between generation and physical execution. Extensive experiments demonstrate that our approach not only improves the physical plausibility of generated motions but also enables more reliable and faithful humanoid interactions in simulation.

Cine cardiovascular magnetic resonance (CMR) captures the cardiac cycle as a four-dimensional (4D) sequence, but standard acquisition requires electrocardiogram (ECG) gating and repeated breath holds. Visual realism alone does not establish accurate patient-specific ejection fraction (EF) or ventricular volumes. We present PhaseFlow3D, a generative framework that synthesizes a complete 4D cine sequence from a single end-diastolic (ED) three-dimensional (3D) volume without ECG. To capture asymmetric systolic and diastolic dynamics, it represents the cardiac cycle as a piecewise linear phase anchored at ED and end-systolic (ES) time points. At inference, a population-level canonical template supplies this phase without patient-specific temporal information. A phase-conditioned rectified flow model generates a cardiac motion trajectory in latent space. Radial Contraction Decomposition converts each latent state into a 3D displacement field, combining a physics-informed radial component for centripetal myocardial contraction with an image-conditioned residual for rotation and out-of-plane motion. Each frame is generated by directly warping the ED volume, bypassing variational autoencoder decoding. On the combined ACDC and M&Ms benchmark, PhaseFlow3D achieves the lowest EF mean absolute error, the only positive left-ventricular volume-curve $R^2$, and the best distributional quality among compared methods. Ablations confirm each component's contribution. Downstream evaluations demonstrate the utility of the synthesized sequences and displacement fields for segmentation, pathology classification, label propagation, and myocardial strain analysis.

Existing methods for 4D hand-object reconstruction often rely on costly per-sequence optimization, while generative approaches typically synthesize interactions from random noise, which can lead to unstable interaction prediction. We introduce 4D-HOF, a feed-forward framework that reconstructs 4D hand-object interactions from coarse but informative estimates produced by vision foundation models. Concretely, we learn a conditional flow matching model that transports foundation-model-derived hand-object states toward an interaction manifold, allowing the model to correct errors in translation, rotation, and alignment in a feed-forward manner. A key advantage of our generative formulation is that it naturally enables test-time guidance within the transport process. Rather than applying a separate post-hoc optimization after reconstruction, we directly steer the evolving generative states using physical interaction constraints and observed 2D evidence, allowing the reconstruction to be refined as part of the generative process itself. By training the generative model on diverse datasets, 4D-HOF generalizes robustly to challenging in-the-wild scenarios. Experiments on out-of-domain benchmarks show that 4D-HOF achieves state-of-the-art performance, producing more stable and accurate 4D hand-object reconstructions.

Realistic physical interaction is a cornerstone of embodied intelligence, yet collecting paired visual--tactile data remains costly. Visual-to-tactile synthesis offers a promising approach to augmenting such data, but learning this mapping is complicated by the gap between visual appearance and contact-related material properties, as well as spatial misalignment in paired observations. To address these challenges, we present \textbf{PhysTacGen}, a visual-to-optical-tactile image generation framework that integrates material-aware descriptions with geometric conditioning. First, we introduce Group Tactile Policy Optimization (GTPO), a reinforcement learning strategy that refines a vision--language model to generate structured material descriptions using task-specific rewards. Second, we combine DINOv2-based pair curation with monocular relative-depth estimation to select training pairs and provide geometric priors. Finally, an SDXL ControlNet synthesizes optical tactile images conditioned on RGB, relative depth, and GTPO-generated text. Experiments on curated SSVTP data demonstrate improved structural similarity over the compared baselines, while a blinded user study shows a preference for GTPO-generated descriptions. Generated tactile inputs also improve performance on an attribute-derived force-coefficient prediction proxy. Together, these results demonstrate the effectiveness of PhysTacGen for optical tactile image synthesis and its utility in the evaluated downstream task.The code will be available at https://github.com/VDIGPKU/PhysTacGen.

Partial differential equation (PDE) inverse problems are often ill-posed, making fine-scale details difficult to recover. We address this problem by introducing a learned observation-complementary latent representation that preserves reconstruction-relevant information and is combined with the observation to reconstruct the unknown field. Building on this representation, we propose OCL-PDE, a generative framework that encourages the observation to guide large-scale structure and the latent to supply complementary fine-scale details. OCL-PDE is built on a physics-aware autoencoder (AE) and conditional Flow Matching, supporting inverse reconstruction as well as forward PDE prediction. Experiments demonstrate improved reconstruction accuracy and fine-detail recovery compared with the evaluated baselines.

Video generation models have achieved remarkable visual fidelity and have strong potential to become general-purpose world simulators. Despite this progress, they still fail to generate videos which adhere to laws of physics. The problem becomes even more apparent in realistic settings where multiple physical principles must work together within the same video; for example, "a balloon floating upward while steam rises from a pot" requires buoyancy and fluid dynamics to unfold coherently and simultaneously. Yet existing methods largely ignore multi-principle interactions, focusing on a single principle per video. We propose HiPhy (Hierarchical Physical Alignment), a reinforcement learning framework that grounds video generation in physical laws through a dual-level objective: locally enforcing the temporal dynamics of individual physical principles, and globally ensuring the physical and semantic coherence of the entire scene. To support multi-principle generation, we construct a 50K-prompt dataset and introduce a prompt benchmark MultiPhyBench, spanning a diverse range of co-occurring physical events. Our experiments show that HiPhy significantly outperforms prior methods and baselines, improving physical commonsense and semantic alignment significantly across various benchmarks, with the largest gains on scenes involving multiple concurrent physical principles where competing methods degrade most sharply.

Generating and predicting spatiotemporal physical fields from scarce measurements is challenging, as observations are insufficient to characterize a distribution over complete fields. This limits conventional data-driven diffusion models that rely on full-field datasets. We introduce PhysDEM, a physics-defined diffusion framework that combines governing equations with spatially sparse observations to generate multiple plausible fields. First, we construct a Gibbs target by reweighting a measurement-conditioned Gaussian reference with PDE residual energy. Second, we derive an exact conditional-mean identity that reduces denoising to supervised learning of the standardized energy-induced mean correction. Third, a physics-displacement probability flow cancels Gaussian reference terms and enables amortized sampling with changing measurements through Gaussian conditioning, without retraining. Experiments on synthetic PDE systems and real-world-informed applications demonstrate that PhysDEM supports coherent field recovery and efficient sampling while maintaining stable diagnostics under tested noise levels, illustrating its practical value for field assessment. To our knowledge, PhysDEM is the first physics-defined diffusion model enabling amortized spatiotemporal field inference without preassembled full-field datasets.

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

Generative models are transforming Bayesian computational imaging, yet the field still lacks physics-aware foundation models. Current practice falls into two camps. Large foundation image models are deployed as plug-and-play priors with zero-shot approximate likelihood guidance, which introduces significant bias and computational cost. Physics-aware generative models avoid this bias, but each is tied to a specific dataset, task and instrument. We introduce BAM (Bayesian Anything Model), a lightweight foundation model for few-step, physics-aware posterior sampling that generalises robustly to unseen data and tasks, zero-shot or with minimal finetuning. BAM upgrades the operator-conditioned Reconstruct Anything Model (RAM) backbone (Terris et al.) into a conditional flow map, so instrument physics is specified at inference time rather than fixed during training. BAM has just 36M parameters and is pre-trained jointly on large image corpora and libraries of forward operators. A single network then draws posterior samples in a few steps, with no likelihood approximation and no guidance weights to tune. Across linear inverse problems on FFHQ, AFHQ, LSUN, DIV2K and the Kohler camera-shake benchmark, BAM outperforms in just 3 steps both specialised models and leading zero-shot methods in sample quality, at a fraction of their computational cost. BAM gives the community an accessible entry point to generative computational imaging, lowers the economic and environmental cost of training imaging models, and opens a new path for research on physics-aware Bayesian computational imaging. Official page: https://bayesian-anything-model.github.io/

Machine learning surrogate models offer a promising path toward accelerating plasma turbulence simulations. We present PreVAE-Turb, a surrogate modeling framework that leverages pre-trained variational autoencoders (VAEs) from the Stable Diffusion image generation model for efficient spatial compression of turbulence fields. The pre-trained VAE is fine-tuned on turbulence data using a physics-informed loss function that includes a spectral loss operating in Fourier space to enforce spectral accuracy across scales. The VAE is combined with convolutional long short-term memory (ConvLSTM) networks to learn temporal dynamics in latent space, with a manifold consistency error metric that monitors encode--decode consistency during autoregressive rollouts. We validate the framework on two-dimensional Hasegawa-Wakatani drift-wave turbulence and extend it to gyrokinetic turbulence from the GENE code, where a four-channel adaptation simultaneously predicts electrostatic potential, density, and parallel/perpendicular temperature fluctuations without requiring architecture redesign. Once trained, inference generates thousands of time steps in seconds on a single GPU, providing substantial computational acceleration compared to direct numerical simulation. The pre-trained approach offers a transferable methodology broadly applicable to various turbulence simulation codes.

We introduce FracGen, a fracture-aware video generation model that produces plausible, controllable fracture dynamics from a single image of an intact object, conditioned on physics signals. To train FracGen, we build FracSim, a fracture-aware simulation framework that augments material point method (MPM) simulation with a continuum damage model, producing paired fracture videos and dense, pixel-aligned physical fields at no additional cost beyond standard rendering. FracGen leverages these maps in two ways: it is trained to jointly predict them alongside RGB video, encouraging the model to capture physical state rather than surface appearance; and it is supervised with physics-informed losses that encourage consistency among the predicted maps. As a result, FracGen captures distinct material-specific fracture behavior without expensive test-time simulation or per-scene tuning, while offering fine-grained control over where an object tears, how fast the crack propagates, and how much deformation precedes failure. We further introduce a benchmark for evaluating the physical plausibility of generated fracture video, and show through extensive experiments that FracGen outperforms existing video generation baselines in both physical and visual fidelity. Results are best viewed in our project website: https://fracgen.github.io/.

Inverse design of physical systems (molecules, devices, microstructures) often reduces to optimizing a high-dimensional structure against an expensive black-box simulator. Direct search is difficult because the space is non-Euclidean, feasibility is hard to encode, and each evaluation is expensive. We present Co-PiLOT, a latent optimization approach that maps candidates through a generative encoder-decoder, uses the decoder as a learned validity prior, and searches the latent space with physics-informed black-box optimization. The framework is applied on the inverse design of magnesium alloy microstructure/texture. We develop a vision transformer based-encoder; paired with latent diffusion, diffusion transformer and rectified-flow transformer-based decoders on $\sim80{,}000$ EBSD-derived microstructure dataset to learn a minimal bottleneck, $z$. The ViT-FMDiT model ($z$=$768$) reconstructs high-fidelity microstructure images (FID $27.86$, MS-SSIM $0.178$), which our self-segmenting orientation codec converts into input grids for crystal plasticity solver. Finally, we introduce MERIDIAN, an active latent optimizer driven by deep-kernel Gaussian-process uncertainty, failure-aware feasibility prediction, manifold-aware trust regions, and target-aware acquisition. Within a budget of $160$ simulations, the ViT-FMDiT and MERIDIAN combination yields the best target-driven objective score, reducing the relative target error by $3$--$22\%$ against seven baselines (DANTE, TuRBO, BAxUS, CMA-ES, DDOM, SEIKO, DDPO) on the same decoder.

Generative models make molecular crystal structure prediction fast, but their samples still exhibit geometric and packing violations. Physics can be introduced during training, post-training, or inference, yet these choices are rarely compared with the generator and physical signal held fixed. We introduce CrystAF, an all-atom crystal flow-map generation model, and use it with the UMA interatomic potential to systematically study where physics should enter. Post-training learns physical preferences directly into CrystAF, improving molecular validity and crystal packing while leaving sampling unchanged: physics is paid for once during training rather than repeatedly at deployment. In contrast, UMA relaxation is effective at repairing local clashes but makes generation 6--26$\times$ slower, while learning from relaxed targets provides little benefit. These routes are complementary rather than competing. Physics-informed post-training first shifts the generated distribution toward more physically reasonable structures, after which inexpensive inference-time corrections further remove clashes and restore stereochemistry that the generator cannot represent. Importantly, the same post-training strategy also improves the multi-step all-atom Clari-M and rigid-body MolCrystalFlow generators, demonstrating transfer across architectures and representations. Together, our results suggest a simple principle: learn reusable physical alignment into the generator, and reserve inference-time physics for residual constraints that are better corrected than learned.

As the world moves towards sustainable energy sources, hydrogen (H2) can be treated as an eco-friendly alternative to fossil fuels due to its high energy density and zero carbon emissions. The water-gas shift (WGS) reaction is a widely used industrial process for hydrogen production by converting carbon monoxide and steam into hydrogen and carbon dioxide. However, occurrences like severe fouling, catalyst deterioration, and thermal runaway can hamper the reaction kinetics/process safety and decrease the yield of H2. These incidents are rare, and gathering process data under such abnormal conditions is challenging. In this work, we propose a physics-guided conditional diffusion model to generate realistic rare-event trajectories for the WGS reaction. The proposed model integrates a conditional denoising diffusion probabilistic model (CDDPM) with governing laws of the reaction to generate physically consistent process trajectories. The conditioning features allow the model to produce high-quality synthetic profiles for rare-event domains that are typically beyond the training regimes. The generated rare-event trajectories then augment the raw dataset for a balanced distribution between normal and abnormal conditions. We further propose a hazard score to assess the risk severity of the operating condition based on the operating trajectory. Deep learning models are trained with the augmented dataset to diagnose the health status of the reaction. Simulation results show that the proposed physics-guided diffusion model outperforms data-driven models in terms of the quality of synthetic data and diagnosis performance for rare events.

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

World models aim to capture environmental dynamics and predict future trajectories, showing growing potential for embodied intelligence. Physics-informed 4D generation integrates physical simulation to predict 3D object interactions, offering a promising pathway toward world models. However, this paradigm relies on manually imposed dynamical assumptions rather than internalizing world dynamics, and thus still leaves a gap toward a true world model. To bridge this gap, we propose NeuIDO, a novel world dynamics modeling framework that learns a unified intrinsic dynamics representation from visual observations, advancing physics-informed 4D generation toward a world model. Specifically, we formulate world modeling as a neural operator learning problem and introduce a two-stage training strategy to learn a generalizable mapping from the visual observation distribution to the intrinsic dynamics distribution. Building on this observation-dynamics mapping, NeuIDO enables zero-shot dynamics inference directly from videos and can be further aligned with complex real-world dynamics via few-shot adaptation. Extensive experiments demonstrate that NeuIDO effectively unifies the intrinsic dynamics underlying diverse visual observations into a shared representation and rapidly infers dynamics in novel scenes.

Internal voids are ubiquitous defects in manufactured structures, yet their characterization remains challenging because their geometry is hidden and can only be inferred indirectly from accessible measurements. Here we introduce \textit{GenVoid}, a physics-informed generative model-based framework for identifying internal voids in complex two- and three-dimensional solids from surface displacement measurements alone. By incorporating the governing mechanics into a generative inference framework, \textit{GenVoid} enables void identification across linear elastic, hyperelastic and plastic material behaviours and accommodates complex two- and three-dimensional structural geometries. Importantly, the framework explicitly accounts for uncertainty and noise in displacement measurements, producing probabilistic reconstructions of internal void geometry rather than a single deterministic estimate. We demonstrate the approach using high-fidelity synthetic datasets and experimentally measured displacement fields obtained from in-situ mechanical experiments, establishing its ability to infer hidden voids from realistic displacement measurements. To quantify the fundamental limits of such inference, we further introduce an observability measure that characterizes the sensitivity of boundary measurements to localized stiffness perturbations within the interior under an ensemble of applied loads. This framework provides a direct connection between defect location, sensor configuration and reconstruction fidelity, enabling systematic assessment of how the number and spatial distribution of boundary measurements govern void-identification accuracy. To this end, these results establish a physics-informed and uncertainty-aware approach for non-invasive characterization of hidden defects and provide a quantitative basis for designing measurement strategies for inverse problems in solid mechanics.

Three-dimensional ultrasound (US) is a safe, radiation-free complementary modality to CT and X-rays for longitudinal monitoring, yet its segmentation-derived partial point clouds are extremely artifact-laden. Consequently, it is challenging to recover a clean and complete anatomical structure from such US point clouds. In this paper, we present UBone3D, a novel framework based on physics-rectified conditional flow matching (CFM) that performs point cloud completion directly from partial US observations. UBone3D models deterministic physics artifacts (e.g., surface thickening, streaking, dropouts) via a simulated physics proxy, and introduces test-time physics rectification to steer the shape completion. At inference, the completion is jointly steered by two decoupled forces: (1) anatomical plausibility enforced by a CT-trained generative shape prior, BoneFM, and (2) physics consistency enforced by USimNet in the ultrasound formation space. Extensive experiments on simulated and in-vivo data demonstrate significant improvements in reconstruction accuracy and anatomical fidelity over existing baselines.

Modern video generators routinely fail at physical dynamics: objects float, trajectories violate gravity, contacts vanish. Standard denoising and flow-matching objectives fit visual data distributions but do not explicitly penalize such physical violations. Existing remedies can improve physical consistency, but typically add substantial inference or training cost. Candidate-selection methods generate and score multiple videos, while gradient-based world-model guidance repeatedly decodes and re-encodes intermediate estimates. Generator-internal refinement adds perturbation and re-denoising loops, whereas post-training requires curated data and additional optimization. We propose Off-Manifold Refinement (OMR), an inference-time method that instead injects world-model feedback directly into a single sampling trajectory. During scheduled middle ODE steps, we augment the generator velocity with the gradient of an adapter-space V-JEPA 2.1 surprise energy. This external correction can move the latent away from the uncorrected sampling trajectory and toward regions ranked as more physically plausible by the frozen predictor, after which the generator continues rendering from the corrected state. A small trained latent-to-embedding adapter keeps the gradient tractable at inference, and both the video generator and the world model remain frozen. On our fixed 400-prompt VideoPhy-2 detailed subset, OMR lifts the joint Semantic-Adherence-and-Physical-Commonsense metric from 47.0% to 52.0% (+5.0pp absolute, +10.6% relative) over the base Wan2.2-T2V-A14B sampler. On a separate fixed 50-prompt efficiency subset, it requires $1.71 \times$ the base runtime rather than the multiplicative cost of reward/search alternatives. Project page: https://itruonghai.github.io/omr.

Streaming world models predict future visual states online while maintaining physically coherent dynamics over long horizons. However, their rollouts often violate basic physical constraints. A common approach distills pretrained bidirectional DiTs into few-step causal generators. However, this paradigm suffers from two fundamental limitations: generic bidirectional teachers acquire limited physical priors from visually oriented pretraining, and the limited priors suffer further loss during bidirectional-to-causal distillation. We present PhyS, a three-stage framework for distilling physical priors into streaming world models. To acquire physical priors from real-world interactions, we construct PhyS-120K, a dataset of 120K real-world physical-interaction videos spanning rigid-body dynamics, soft-body deformation, fluid phenomena, and phase transitions. Each video is annotated with structured descriptions of object properties and causal state transitions. Physics-aware supervised fine-tuning injects the physical priors into a bidirectional 14B DiT teacher, which we then distill into a lightweight 1.3B causal DiT for few-step autoregressive streaming generation. Finally, we use online reinforcement learning to incentivize the distilled model to generate physically plausible rollouts and further propose Temporal Credit Routing (TCR) to address temporal credit assignment. TCR evaluates physical consistency over overlapping temporal windows and routes the resulting group-relative advantages to temporally aligned denoising actions. On PhysicsIQ, PhyS improves the Wan2.1-14B teacher by 18.2% and the Self Forcing, Rolling Forcing, and Causal Forcing by 23.7%, 14.8%, and 31.4%, respectively. Results also improve the physics-aware video benchmarks VideoPhy, VideoPhy2, and PhyGenBench. The dataset, code, and more sample videos are available on our Project Page.

Developing robust flood assessment models requires high-quality paired satellite imagery, yet such data remain scarce for flood-specific image generation. Although generative models provide a promising means of data augmentation, existing methods often yield implausible spatial layouts of flooded regions and distort scene structures. We propose FlowForm, a framework for satellite flood synthesis that integrates SWE-inspired latent regularization with structure-aware conditioning. The Flood Descriptor Module (FDM) imposes differentiable penalties on residuals of the steady-state Shallow Water Equation in auxiliary latent fields at the diffusion bottleneck. The Terrain Anchor Adapter (TAA) injects depth, semantic, and edge features at four encoder scales of the U-Net. We further curate FloodScape, a large-scale, high-resolution dataset comprising paired satellite images acquired before and after disasters. In addition to standard image-generation metrics, we evaluate the consistency of flooded regions, zero-shot generalization to a geographically held-out flood event, and sensitivity to individual components. Across all reported comparisons, FlowForm achieves higher visual fidelity, greater similarity between paired images, and stronger consistency of flooded regions.

Monte Carlo simulation of calorimeter showers is a principal bottleneck for the High-Luminosity LHC, and diffusion models have emerged as fast, high-fidelity surrogates. Their denoising objective is purely statistical, however: a model can minimize it while placing the physics wrong. Existing physics-informed generative methods cannot close this gap, because they assume a closed-form law, a governing PDE residual or a hard per-sample constraint, that a shower does not supply: no per-sample PDE governs a stochastic cascade, and energy conservation fixes only one scalar per shower. Standard metrics ignore the correlation structure across calorimeter layers and voxels, comparing showers only in a physics feature space. We address both gaps. We introduce the Correlation Frobenius Distance (CFD), a single normalized score for correlation fidelity at layer-wise and voxel-wise scales. We then encode the soft per-sample structure available in a shower as two physics-aware auxiliary losses: a variance-stabilized voxel residual loss grounded in counting statistics, and a graph Laplacian loss over the detector geometry. We combine both with denoising through GradBlend, which anchors the step magnitude to the denoising gradient while letting the auxiliary steer its direction, yielding Lantern, a physics-guided diffusion surrogate. On CaloChallenge Dataset 2, injecting the physics losses through task-symmetric rules such as PCGrad, GradNorm, IMTL-G, and ConFIG inflates FPD by 2-100x relative to denoising alone, whereas GradBlend admits the same signal without regression and, with the Laplacian loss, Lantern improves both FPD and CFD. Our ablation on the auxiliary loss scheduler shows that the voxel residual loss, whose gradient conflicts with denoising, requires a terminal denoising-only phase to preserve shower fidelity, whereas the non-conflicting Laplacian loss is insensitive to the schedule.

Video generation models achieve high visual quality but often struggle to generate physics-aware videos. Unlike rigid-body motion, which can be described by explicit trajectories or formulas, complex deformation dynamics remain challenging to synthesize. We observe that a lack of physical reasoning for localizing dynamic areas allows irrelevant regions to dilute the model's attention, leading to generation failure. In this paper, we propose DeforM, a reasoning-guided image-to-video generation framework that directs the model's focus toward physics-critical regions. To reason about and localize these critical regions, we introduce a VLM-guided physical reasoning module, DeforM-Reason, to identify target objects and generate spatial-temporal masks. For physical guidance, we develop two alternative strategies: DeforM-Free for training-free mechanism analysis and DeforM-Injection as a powerful training-based generator. Experimental results demonstrate that DeforM improves the realism of generated deformation scenarios, outperforming baseline models in both visual quality and physical consistency.

Accurately modeling the dynamics of planetary parachute and entry vehicle systems is critical for Entry, Descent, and Landing events such as vehicle separation and sensor activation. These dynamics are difficult to capture with traditional system-identification methods as parachute motion is highly nonlinear, the governing equations are not fully known, and relevant test data are scarce and expensive to acquire. In this work, we sidestep these challenges by leveraging a physics-aware generative modeling approach that learns parachute dynamics directly from data. The proposed method, Symplectic Parachute Generative Adversarial Network (SPar-GAN), adapts a Hamiltonian generative architecture to the parachute setting by conditioning on canopy design and freestream velocity, while enforcing conservation of energy through symplectic integration. We apply SPar-GAN to subscale parachute tests conducted at the National Full-Scale Aerodynamics Complex and show that it reproduces qualitatively accurate pitch-yaw dynamics of different parachute configurations while recovering a compact two-degree-of-freedom phase-space consistent with canopy axisymmetry. These results suggest that physics-constrained generative models can characterize parachute dynamics across operating conditions and may help reduce the volume of physical testing required to assess performance.

Generative models have emerged as scalable surrogates for physical simulation, yet they offer no guarantee that their outputs respect the conservation laws, boundary conditions, and nonlinear invariants that govern the underlying physics. Constrained sampling closes this gap, enforcing such constraints exactly at inference time without retraining, but at a computational cost: projection, correction and trajectory-optimization steps are repeated during sampling, with these steps becoming expensive for nonlinear constraints. Standard ML frameworks exacerbate this: their dense tensor algebra and limited sparse solver composability obscure the structure that physical constraints naturally induce, making efficient batched nonlinear optimization difficult to realize in practice. We address this bottleneck by exploiting the structure that sample-wise batching and local PDE couplings induce in the projection subproblems -- namely, block-sparse Jacobian and KKT systems -- exposing this structure using ExaModels.jl and solving the resulting sparse nonlinear programs with MadNLP.jl and GPU sparse factorization. Applied to Physics-Constrained Flow Matching (PCFM), on PDE benchmarks with linear, nonlinear, one-dimensional, and two-dimensional constraints, this approach accelerates nonlinear constraint projection while maintaining constraint satisfaction. These results show that sparse GPU nonlinear optimization is a practical foundation for constrained generative sampling in scientific machine learning.

Reliable extrapolation remains a central challenge for generative models in computational physics, because models trained over finite ranges of time, parameters, or geometries may produce physically inconsistent predictions outside the training distribution. We introduce a least-action-principle-guided diffusion, LAPG, a framework that promotes physical consistency during inference rather than relying solely on constraints imposed during training. The method combines a conditional score-based diffusion model with an action-derived physical guidance score. In the first stage, the learned score model generates an in-distribution proposal; in the second, an action-based variational prior refines this proposal toward the target out-of-distribution condition. This formulation turns the principle of least action into a differentiable inference-time correction mechanism and provides an alternative to pointwise residual penalties that often require empirical loss balancing. We evaluate LAPG on representative ordinary- and partial-differential-equation systems, including free fall, conservative and dissipative spring-mass dynamics, interacting point vortices, and potential flow over parameterized airfoils. In temporal, parameter, and geometric extrapolation tests, LAPG reduces phase drift, preserves dissipative decay, captures vortex motion, and improves the lift response of airfoil flows compared with training-time physics-informed baselines.

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.

Metasurfaces enable precise manipulation of electromagnetic waves for applications such as beam steering, sensing, and stealth technology. However, inverse design of metasurfaces with targeted EM responses remains challenging due to the computational expense of iterative full wave simulation driven optimization and the limited conditioning fidelity and diversity of existing generative approaches. To address these challenges, this paper presents a generative inverse design framework for controllable and physically consistent metasurface synthesis under continuous spectral constraints. The proposed approach employs a progressively growing Wasserstein generative adversarial network with gradient penalty integrated with feature wise linear modulation based conditioning for stable propagation of continuous spectral and fabrication constraints. EM consistency is embedded directly into the generative learning process through a surrogate assisted spectral alignment loss, enabling physics constrained generation during training. Further, a determinantal point process based diversity regularization strategy is incorporated to generate geometrically diverse yet spectrally consistent realizations for the same target response. The effectiveness of the proposed framework is demonstrated through the generation of practically realizable metasurface absorbers exhibiting diverse reflection characteristics in the frequency range of 2 to 18 GHz. EM simulations validate that the generated designs meet the target specifications with high accuracy. The final proposed framework achieved an average mean squared error of 0.0052, diversity score of 0.8730, band alignment accuracy of 0.8533, and a valid EM design generation percentage of 89.57, clearly demonstrating its capability to generate highly accurate, diverse, electromagnetically consistent and fabrication realizable metasurface configurations.

Generative models -- diffusion and flow matching -- are increasingly used to solve partial differential equation (PDE) inverse problems, enforcing the governing physics as a \emph{hard constraint} (via projection or guidance) and reporting the resulting samples as a Bayesian posterior with calibrated uncertainty. We show that this widely adopted recipe samples the wrong distribution. Conditioning a generative prior on a hard PDE constraint is conditioning on a measure-zero manifold -- an operation that is intrinsically ambiguous (the Borel--Kolmogorov paradox) and whose physically correct resolution, the small-residual-noise limit, carries a co-area (Fixman) Jacobian factor $[det(JJ^{\top})]^{-1/2}$ that projection- and guidance-based methods silently omit. We make the bias precise, show that it grows with the heterogeneity of the constraint sensitivity, and validate it on controlled problems against an \emph{i.i.d.} ground-truth arbiter. The omitted factor is not a second-order detail: removing it inflates the posterior error to $20\times$ the sampling-noise floor; minimal-displacement projection (as in PCFM) is biased at $9\times$ the floor; and a naive scalar reweighting does not fix it. We introduce \textbf{CoCoS}, a measure-aware constrained sampler that targets the correct co-area posterior, and show that it matches the gold-standard posterior to within sampling noise. Our results imply that satisfying the physics'' is not the same as sampling the posterior,'' and give a principled correction for uncertainty-aware scientific inference.

Large-scale video generation models have made remarkable progress in semantic consistency and visual quality, producing videos that are increasingly coherent and visually convincing. Nevertheless, the dynamics induced by pixel-level fitting do not naturally accommodate the regularities that govern real-world motion and interaction, resulting in persistent shortcomings in physical plausibility. To address this limitation, we propose \textbf{PILA} (Physics-Informed Latent Alignment), a framework that injects physics-structured latent guidance into the frozen flow-matching dynamics of pretrained video models. Specifically, PILA first employs anchored field estimation to map frozen-generator latents into an operational physical attribute bank organized by field-proxy slots, using observable motion as a kinematic anchor for constructing less directly observed proxies. To handle the heterogeneity of real-world dynamics, PILA adopts a mixture-of-experts design over physical categories. Label-prior masked expert routing selects category-specific operator experts, whose refinements are regularized by operational residuals abstracted from physical relations. Finally, the refined proxies are fused into the physical attribute bank and decoded into a correction to the flow-matching vector field, injecting physics-aware guidance while preserving the visual prior of the pretrained backbone. With staged adapter training on Wan 2.1-1.3B and direct transfer of the learned adapter to Wan 2.2-14B, PILA achieves state-of-the-art results on VBench-2.0, VideoPhy-2, and PhyGenBench in both visual quality and benchmark-measured physical plausibility.