Inverse Problems

We establish guarantees for the unique recovery of vector fields and transport maps from finite measure-valued data, yielding new insights into generative models, data-driven dynamical systems, and PDE inverse problems. In particular, we provide general conditions under which a diffeomorphism can be uniquely identified from its pushforward action on finitely many densities, i.e., when the data $\{(ρ_j,f_\#ρ_j)\}_{j=1}^m$ uniquely determines $f$. As a corollary, we introduce a new metric which compares diffeomorphisms by measuring the discrepancy between finitely many pushforward densities in the space of probability measures. We also prove analogous results in an infinitesimal setting, where derivatives of the densities along a smooth vector field are observed, i.e., when $\{(ρ_j,\text{div} (ρ_j v))\}_{j=1}^m$ uniquely determines $v$. Our analysis makes use of the Whitney and Takens embedding theorems, which provide estimates on the required number of densities $m$, depending only on the intrinsic dimension of the problem. We additionally interpret our results through the lens of Perron--Frobenius and Koopman operators and demonstrate how our techniques lead to new guarantees for the well-posedness of certain PDE inverse problems related to continuity, advection, Fokker--Planck, and advection-diffusion-reaction equations. Finally, we present illustrative numerical experiments demonstrating the unique identification of transport maps from finitely many pushforward densities, and of vector fields from finitely many weighted divergence observations.

Full-waveform inversion (FWI) is pivotal for reconstructing high-resolution subsurface velocity models but remains computationally intensive and ill-posed. While deep learning approaches promise efficiency, existing Convolutional Neural Networks (CNNs) and single-paradigm Neural Operators (NOs) struggle with one fundamental issue: frequency entanglement of multi-scale geological features. To address this challenge, we propose Spectral-Preserving Adaptive MoE (SPAMoE), a novel spectrum-aware framework for solving inverse problems with complex multi-scale structures. Our approach introduces a Spectral-Preserving DINO Encoder that enforces a lower bound on the high-to-low frequency energy ratio of the encoded representation, mitigating high-frequency collapse and stabilizing subsequent frequency-domain modeling. Furthermore, we design a novel Spectral Decomposition and Routing mechanism that dynamically assigns frequency bands to a Mixture-of-Experts (MoE) ensemble comprising FNO, MNO, and LNO. On the ten OpenFWI sub-datasets, experiments show that SPAMoE reduces the average MAE by 44.4% relative to the best officially reported OpenFWI baseline, thereby establishing a new architectural framework for learning-based full-waveform inversion. Our code and data are available at https://github.com/zhenyuwang12366/SPAMoE

Accurate knowledge of acoustic surface admittance or impedance is essential for reliable wave-based simulations, yet its in situ estimation remains challenging due to noise, model inaccuracies, and restrictive assumptions of conventional methods. This work presents a physics-informed neural operator approach for estimating frequency-dependent surface admittance directly from near-field measurements of sound pressure and particle velocity. A deep operator network is employed to learn the mapping from measurement data, spatial coordinates, and frequency to acoustic field quantities, while simultaneously inferring a globally consistent surface admittance spectrum without requiring an explicit forward model. The governing acoustic relations, including the Helmholtz equation, the linearized momentum equation, and Robin boundary conditions, are embedded into the training process as physics-based regularization, enabling physically consistent and noise-robust predictions while avoiding frequency-wise inversion. The method is validated using synthetically generated data from a simulation model for two planar porous absorbers under semi free-field conditions across a broad frequency range. Results demonstrate accurate reconstruction of both real and imaginary admittance components and reliable prediction of acoustic field quantities. Parameter studies confirm improved robustness to noise and sparse sampling compared to purely data-driven approaches, highlighting the potential of physics-informed neural operators for in situ acoustic material characterization.

Accurate reconstruction of environmental scalar fields from sparse onboard observations is essential for autonomous vehicles engaged in aquatic monitoring. Beyond point estimates, principled uncertainty quantification is critical for active sensing strategies such as Informative Path Planning, where epistemic uncertainty drives data collection decisions. This paper compares Gaussian Processes, Monte Carlo Dropout, Deep Ensembles, and Evidential Deep Learning for simultaneous scalar field reconstruction and uncertainty decomposition under three perceptual models representative of real sensor modalities. Results show that Evidential Deep Learning achieves the best reconstruction accuracy and uncertainty calibration across all sensor configurations at the lowest inference cost, while Gaussian Processes are fundamentally limited by their stationary kernel assumption and become intractable as observation density grows. These findings support Evidential Deep Learning as the preferred method for uncertainty-aware field reconstruction in real-time autonomous vehicle deployments.

Editing animatable human avatars typically relies on sparse supervision, often a few edited keyframes, yet naively fitting a reconstructed avatar to these edits frequently causes identity leakage and pose-dependent temporal flicker. We argue that these failures are best understood as an ill-conditioned inversion: the available edited constraints do not sufficiently determine the latent directions responsible for the intended edit. We propose a conditioning-guided edited reconstruction framework that performs editing as a constrained inversion in a structured avatar latent space, restricting updates to a low-dimensional, part-specific edit subspace to prevent unintended identity changes. Crucially, we design the editing constraints during inversion by optimizing a conditioning objective derived from a local linearization of the full decoding-and-rendering pipeline, yielding an edit-subspace information matrix whose spectrum predicts stability and drives frame reweighting / keyframe activation. The resulting method operates on small subspace matrices and can be implemented efficiently (e.g., via Hessian-vector products), and improves stability under limited edited supervision.

We address the inverse problem of designing two-dimensional reflectors that transform light from a finite, extended source into a prescribed far-field distribution. The reflector height is represented by a neural network and optimized with two objective functions: a direct change-of-variables loss based on the closed-form inverse ray map, and a mesh-based loss that maps target cells back to the source and remains usable for discontinuous sources. Gradients are computed by automatic differentiation and minimized with a robust quasi-Newton method. As a baseline, we adapt a deconvolution pipeline built on a simplified finite-source approximation: a one-dimensional monotone map is recovered from flux balance, converted to a reflector by an integrating-factor ODE solve, and embedded in a modified Van Cittert iteration with nonnegativity clipping and ray-traced feedback. Across four benchmarks, covering continuous and discontinuous sources and minimum-height constraints, accuracy is measured by ray-traced normalized mean absolute error. On the two main benchmarks, the neural method reaches errors of about 2e-5 and 5e-5 within a few seconds on one NVIDIA RTX 4090 GPU, compared with 4e-3 and 5e-2 for the deconvolution baseline after several hundred seconds. The results show that the neural formulation is both more accurate and substantially faster, while still supporting practical height constraints. We also discuss extensions to rotationally symmetric and full three-dimensional reflector design through iterative correction schemes.

Physics-driven 4D dynamic simulation from static 3D scenes remains constrained by an overlooked contradiction: reliable motion supervision often relies on online video diffusion or optical-flow pipelines whose computational cost exceeds that of the simulator itself. Existing methods further simplify inverse physical modeling by optimizing only partial material parameters, limiting realism in scenes with complex materials and dynamics. We present Resonance4D, a physics-driven 4D dynamic simulation framework that couples 3D Gaussian Splatting with the Material Point Method through lightweight yet physically expressive supervision. Our key insight is that dynamic consistency can be enforced without dense temporal generation by jointly constraining motion in complementary domains. To this end, we introduce Dual-domain Motion Supervision (DMS), which combines spatial structural consistency for local deformation with frequency-domain spectral consistency for oscillatory and global dynamic patterns, substantially reducing training cost and memory overhead while preserving physically meaningful motion cues. To enable stable full-parameter physical recovery, we further combine zero-shot text-prompted segmentation with simulation-guided initialization to automatically decompose Gaussians into object-part-level regions and support joint optimization of full material parameters. Experiments on both synthetic and real scenes show that Resonance4D achieves strong physical fidelity and motion consistency while reducing peak GPU memory from over 35,GB to around 20,GB, enabling high-fidelity physics-driven 4D simulation on a single consumer-grade GPU.

Recent advances in generative networks have enabled new approaches to subsurface velocity model synthesis, offering a compelling alternative to traditional methods such as Full Waveform Inversion. However, these approaches predominantly rely on the availability of large-scale datasets of high-quality, geologically realistic subsurface velocity models, which are often difficult to obtain in practice. We introduce SAGE, a novel framework for statistically consistent proxy velocity generation from incomplete observations, specifically sparse well logs and migrated seismic images. During training, SAGE learns a proxy posterior over velocity models conditioned on both modalities (wells and seismic); at inference, it produces full-resolution velocity fields conditioned solely on migrated images, with well information implicitly encoded in the learned distribution. This enables the generation of geologically plausible and statistically accurate velocity realizations. We validate SAGE on both synthetic and field datasets, demonstrating its ability to capture complex subsurface variability under limited observational constraints. Furthermore, samples drawn from the learned proxy distribution can be leveraged to train downstream networks, supporting inversion workflows. Overall, SAGE provides a scalable and data-efficient pathway toward learning geological proxy posterior for seismic imaging and inversion. Repo link: https://github.com/slimgroup/SAGE.

Cameras capture scene-referred linear raw images, which are processed by onboard image signal processors (ISPs) into display-referred 8-bit sRGB outputs. Although raw data is more faithful for low-level vision tasks, collecting large-scale raw datasets remains a major bottleneck, as existing datasets are limited and tied to specific camera hardware. Generative models offer a promising way to address this scarcity -- however, existing diffusion frameworks are designed to synthesize photo-finished sRGB images rather than physically consistent linear representations. This paper presents RawGen, to our knowledge the first diffusion-based framework enabling text-to-raw generation for arbitrary target cameras, alongside sRGB-to-raw inversion. RawGen leverages the generative priors of large-scale sRGB diffusion models to synthesize physically meaningful linear outputs, such as CIE XYZ or camera-specific raw representations, via specialized processing in latent and pixel spaces. To handle unknown and diverse ISP pipelines and photo-finishing effects in diffusion-model training data, we build a many-to-one inverse-ISP dataset where multiple sRGB renditions of the same scene generated using diverse ISP parameters are anchored to a common scene-referred target. Fine-tuning a conditional denoiser and specialized decoder on this dataset allows RawGen to obtain camera-centric linear reconstructions that effectively invert the rendering pipeline. We demonstrate RawGen's superior performance over traditional inverse-ISP methods that assume a fixed ISP. Furthermore, we show that augmenting training pipelines with RawGen's scalable, text-driven synthetic data can benefit downstream low-level vision tasks.

In this paper, we present a novel variational plug-and-play algorithm for Poisson inverse problems. Our approach minimizes an explicit functional which is the sum of a Kullback-Leibler data fidelity term and a regularization term based on a pre-trained neural network. By combining classical likelihood maximization methods with recent advances in gradient-based denoisers, we allow the use of pre-trained Gaussian denoisers without sacrificing convergence guarantees. The algorithm is formulated in the majorization-minimization framework, which guarantees convergence to a stationary point. Numerical experiments confirm state-of-the-art performance in deconvolution and tomography under moderate noise, and demonstrate clear superiority in high-noise conditions, making this method particularly valuable for nuclear medicine applications.

Full-waveform inversion (FWI) estimates physical parameters in the wave equation from limited measurements and has been widely applied in geophysical exploration, medical imaging, and non-destructive testing. Conventional FWI methods are limited by their notorious sensitivity to the accuracy of the initial models. Recent progress in continuous representation FWI (CR-FWI) demonstrates that representing parameter models with a coordinate-based neural network, such as implicit neural representation (INR), can mitigate the dependence on initial models. However, its underlying mechanism remains unclear, and INR-based FWI shows slower high-frequency convergence. In this work, we investigate the general CR-FWI framework and develop a unified theoretical understanding by extending the neural tangent kernel (NTK) for FWI to establish a wave-based NTK framework. Unlike standard NTK, our analysis reveals that wave-based NTK is not constant, both at initialization and during training, due to the inherent nonlinearity of FWI. We further show that the eigenvalue decay behavior of the wave-based NTK can explain why CR-FWI alleviates the dependency on initial models and shows slower high-frequency convergence. Building on these insights, we propose several CR-FWI methods with tailored eigenvalue decay properties for FWI, including a novel hybrid representation combining INR and multi-resolution grid (termed IG-FWI) that achieves a more balanced trade-off between robustness and high-frequency convergence rate. Applications in geophysical exploration on Marmousi, 2D SEG/EAGE Salt and Overthrust, 2004 BP model, and the more realistic 2014 Chevron models show the superior performance of our proposed methods compared to conventional FWI and existing INR-based FWI methods.

Phase unwrapping remains a critical and challenging problem in InSAR processing, particularly in scenarios involving complex deformation patterns. In earthquake-related deformation, shallow sources can generate surface-breaking faults and abrupt displacement discontinuities, which severely disrupt phase continuity and often cause conventional unwrapping algorithms to fail. Another limitation of existing learning-based unwrapping methods is their reliance on fixed and relatively small input sizes, while real InSAR interferograms are typically large-scale and spatially heterogeneous. This mismatch restricts the applicability of many neural network approaches to real-world data. In this work, we present a phase unwrapping framework based on a diffusion model, developed to process large-scale interferograms and to address phase discontinuities caused by deformation. By leveraging a diffusion model architecture, the proposed method can recover physically consistent unwrapped phase fields even in the presence of fault-related phase jumps. Experimental results on both synthetic and real datasets demonstrate that the method effectively addresses discontinuities associated with near-surface deformation and scales well to large InSAR images, offering a practical alternative to manual unwrapping in challenging scenarios.

Solving ill-posed inverse problems necessitates effective regularization strategies to stabilize the inversion process against measurement noise. While classical methods like Tikhonov regularization require heuristic parameter tuning, and standard deep learning approaches often lack interpretability and generalization across resolutions, we propose SC-Net (Spectral Correction Network), a novel operator learning framework. SC-Net operates in the spectral domain of the forward operator, learning a pointwise adaptive filter function that reweights spectral coefficients based on the signal-to-noise ratio. We provide a theoretical analysis showing that SC-Net approximates the continuous inverse operator, guaranteeing discretization invariance. Numerical experiments on 1D integral equations demonstrate that SC-Net: (1) achieves the theoretical minimax optimal convergence rate ($O(δ^{0.5})$ for $s=p=1.5$), matching theoretical lower bounds; (2) learns interpretable sharp-cutoff filters that outperform Oracle Tikhonov regularization; and (3) exhibits zero-shot super-resolution, maintaining stable reconstruction errors ($\approx 0.23$) when trained on coarse grids ($N=256$) and tested on significantly finer grids (up to $N=2048$). The proposed method bridges the gap between rigorous regularization theory and data-driven operator learning.

Learned priors based on deep generative models offer data-driven regularization for seismic inversion, but training them requires a dataset of representative subsurface models -- a resource that is inherently scarce in geoscience applications. Since the training objective of most generative models can be cast as maximum likelihood on a finite dataset, any such model risks converging to the empirical distribution -- effectively memorizing the training examples rather than learning the underlying geological distribution. We show that the posterior under such a memorized prior reduces to a reweighted empirical distribution -- i.e., a likelihood-weighted lookup among the stored training examples. For diffusion models specifically, memorization yields a Gaussian mixture prior in closed form, and linearizing the forward operator around each training example gives a Gaussian mixture posterior whose components have widths and shifts governed by the local Jacobian. We validate these predictions on a stylized inverse problem and demonstrate the consequences of memorization through diffusion posterior sampling for full waveform inversion.

We study the ill-posed problem of recovering a probability measure flow from finitely many moving localized sensors using a Bayes Hilbert framework. Relative to a fixed reference probability measure, a probability law is represented by its centered log-ratio coordinates, so that an evolving law becomes a path in a Hilbert space of functions. For sufficiently regular Bayes Hilbert paths, we construct a canonical minimum-energy transport realization of the path by solving a weighted Neumann problem at each time, yielding an intrinsic transport form on tangent directions. We then formulate an inverse problem directly on Bayes Hilbert path space. Linearization of an observation operator yields an observability form, and recoverability is governed by its interaction with the transport geometry through a joint transport--observability form. In the ambient infinite-dimensional setting, we develop a regularized variational theory and identify limitations of localized sensing: mobile sensors can make the joint form injective, but they do not in general yield a coercive stability estimate on the full state space. This obstruction leads naturally to finite-dimensional Bayes Hilbert reductions. There the transport form becomes a kinetic tensor and the linearized observations become reduced sensing matrices, so recoverability can be expressed through explicit Gramian conditions. We show that localized bump sensors detect every fixed reduced direction, that finitely many suitably placed static sensors yield uniform reduced observability, and there exist path-dependent sensor trajectories such that even a single moving sensor can recover the reduced path. Finally, we show that these reduced recovery results lift to approximate ambient recovery for paths that are well approximated by the chosen finite-dimensional subspaces, yielding stable reconstruction up to projection error.

Bayesian inference represents a principled way to incorporate Earth structure uncertainty in full-waveform moment tensor inversions, but traditional approaches generally require significant approximations that risk biasing the resulting solutions. We introduce a robust method for handling theory errors using simulation-based inference (SBI), a machine learning approach that empirically models their impact on the observations. This framework retains the rigour of Bayesian inference while avoiding restrictive assumptions about the functional form of the uncertainties. We begin by demonstrating that the common Gaussian parametrisation of theory errors breaks down under minor ($1-3 \%$) 1-D Earth model uncertainty. To address this issue, we develop two formalisms for utilising SBI to improve the quality of the moment tensor solutions: one using physics-based insights into the theory errors, and another utilising an end-to-end deep learning algorithm. We then compare the results of moment tensor inversion with the standard Gaussian approach and SBI, and demonstrate that Gaussian assumptions induce bias and significantly under-report moment tensor uncertainties. We also show that these effects are particularly problematic when inverting short period data and for shallow, isotropic events. On the other hand, SBI produces more reliable, better calibrated posteriors of the earthquake source mechanism. Finally, we successfully apply our methodology to two well studied moderate magnitude earthquakes: one from the 1997 Long Valley Caldera volcanic earthquake sequence, and the 2020 Zagreb earthquake.

Seismic full-waveform inversion is a core technology for obtaining high-resolution subsurface model parameters. However, its highly nonlinear characteristics and strong dependence on the initial model often lead to the inversion process getting trapped in local minima. In recent years, generative diffusion models have provided a way to regularize full-waveform inversion by learning implicit prior distributions. However, existing methods mostly use unconditional diffusion processes, ignoring the inherent physical coupling relationship between velocity and density and other physical properties. This paper proposes a full-waveform inversion method based on conditional diffusion model regularization. By improving the backbone network structure of the diffusion model, two-dimensional density information is introduced as a conditional input into the U-Net network. Experimental results show that the full-waveform inversion method based on the conditional diffusion model significantly improves the resolution and structural fidelity of the inversion results, and exhibits stronger stability and robustness when dealing with complex situations. This method effectively utilizes density information to constrain the inversion and has good practical application value. Keywords: Deep learning; Diffusion model; Full waveform inversion.

Estimating time-varying reproduction numbers from epidemic incidence data is a central task in infectious disease surveillance, yet it poses an inherently ill-posed inverse problem. Existing approaches often rely on strong structural assumptions derived from epidemiological models, which can limit their ability to adapt to non-stationary transmission dynamics induced by interventions or behavioral changes, leading to delayed detection of regime shifts and degraded estimation accuracy. In this work, we propose a Conditional Inverse Reproduction Learning framework (CIRL) that addresses the inverse problem by learning a {conditional mapping} from historical incidence patterns and explicit time information to latent reproduction numbers. Rather than imposing strongly enforced parametric constraints, CIRL softly integrates epidemiological structure with flexible likelihood-based statistical modeling, using the renewal equation as a forward operator to enforce dynamical consistency. The resulting framework combines epidemiologically grounded constraints with data-driven temporal representations, producing reproduction number estimates that are robust to observation noise while remaining responsive to abrupt transmission changes and zero-inflated incidence observations. Experiments on synthetic epidemics with controlled regime changes and real-world SARS and COVID-19 data demonstrate the effectiveness of the proposed approach.

Gradient inversion attacks reveal that private training text can be reconstructed from shared gradients, posing a privacy risk to large language models (LLMs). While prior methods perform well in small-batch settings, scaling to larger batch sizes and longer sequences remains challenging due to severe signal mixing, high computational cost, and degraded fidelity. We present SOMP (Subspace-Guided Orthogonal Matching Pursuit), a scalable gradient inversion framework that casts text recovery from aggregated gradients as a sparse signal recovery problem. Our key insight is that aggregated transformer gradients retain exploitable head-wise geometric structure together with sample-level sparsity. SOMP leverages these properties to progressively narrow the search space and disentangle mixed signals without exhaustive search. Experiments across multiple LLM families, model scales, and five languages show that SOMP consistently outperforms prior methods in the aggregated-gradient regime.For long sequences at batch size B=16, SOMP achieves substantially higher reconstruction fidelity than strong baselines, while remaining computationally competitive. Even under extreme aggregation (up to B=128), SOMP still recovers meaningful text, suggesting that privacy leakage can persist in regimes where prior attacks become much less effective.

Unsupervised physical parameter estimation from video lacks a common benchmark: existing methods evaluate on non-overlapping synthetic data, the sole real-world dataset is restricted to single-body systems, and no established protocol addresses governing-equation identification. This work introduces IRIS, a high-fidelity benchmark comprising 240 real-world videos captured at 4K resolution and 60fps, spanning both single- and multi-body dynamics with independently measured ground-truth parameters and uncertainty estimates. Each dynamical system is recorded under controlled laboratory conditions and paired with its governing equations, enabling principled evaluation. A standardized evaluation protocol is defined encompassing parameter accuracy, identifiability, extrapolation, robustness, and governing-equation selection. Multiple baselines are evaluated, including a multi-step physics loss formulation and four complementary equation-identification strategies (VLM temporal reasoning, describe-then-classify prompting, CNN-based classification, and path-based labelling), establishing reference performance across all IRIS scenarios and exposing systematic failure modes that motivate future research. The dataset, annotations, evaluation toolkit, and all baseline implementations are publicly released.

We develop a robust physics-guided diffusion framework for full-waveform inversion that combines a score-based generative prior with likelihood guidance computed through wave-equation simulations. We adopt a transport-based data-consistency potential (Wasserstein-2), incorporating wavefield enhancement via bounded weighting and observation-dependent normalization, thereby improving robustness to amplitude imbalance and time/phase misalignment. On the inference side, we introduce a preconditioned guided reverse-diffusion scheme that adapts the guidance strength and spatial scaling throughout the reverse-time dynamics, yielding a more stable and effective data-consistency guidance step than standard diffusion posterior sampling (DPS). Numerical experiments on OpenFWI datasets demonstrate improved reconstruction quality over deterministic optimization baselines and standard DPS under comparable computational budgets.

Seismic inversion is a core problem in geophysical exploration, where traditional methods suffer from high computational costs and are susceptible to initial model dependence. In recent years, deep generative model-based seismic inversion methods have achieved remarkable progress, but existing generative models struggle to balance sampling efficiency and inversion accuracy. This paper proposes an end-to-end fast seismic inversion method based on Conditional Rectified Flow[1], which designs a dedicated seismic encoder to extract multi-scale seismic features and adopts a layer-by-layer injection control strategy to achieve fine-grained conditional control. Experimental results demonstrate that the proposed method achieves excellent inversion accuracy on the OpenFWI[2] benchmark dataset. Compared with Diffusion[3,4] methods, it achieves sampling acceleration; compared with InversionNet[5,6,7] methods, it achieves higher accuracy in generation. Our zero-shot generalization experiments on Marmousi[8,9] real data further verify the practical value of the method. Experimental results show that the proposed method achieves excellent inversion accuracy on the OpenFWI benchmark dataset; compared with Diffusion methods, it achieves sampling acceleration while maintaining higher accuracy than InversionNet methods; experiments based on the Marmousi standard model further verify that this method can generate high-quality initial velocity models in a zero-shot manner, effectively alleviating the initial model dependency problem in traditional Full Waveform Inversion (FWI), and possesses industrial practical value.

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.

Full-waveform inversion (FWI) is a high-resolution seismic imaging method that estimates subsurface velocity by matching simulated and recorded waveforms. However, FWI is highly nonlinear, prone to cycle skipping, and sensitive to noise, particularly when low frequencies are missing or the initial model is poor, leading to failures under imperfect acquisition. Diffusion-regularized FWI introduces generative priors to encourage geologically realistic models, but these priors typically require costly offline pretraining and can deteriorate under distribution shift. Moreover, they assume Gaussian initialization and a fixed noise schedule, in which it is unclear how to map a deterministic FWI iterate and its starting model to a well-defined diffusion time or noise level. To address these limitations, we introduce Self-Flow-Matching assisted Full-Waveform Inversion (SFM-FWI), a physics-driven framework that eliminates the need for large-scale offline pretraining while avoiding the noise-level alignment ambiguity. SFM-FWI leverages flow matching to learn a transport field without assuming Gaussian initialization or a predefined noise schedule, so the initial model can be used directly as the starting point of the dynamics. Our approach trains a single flow network online using the governing physics and observed data. At each outer iteration, we build an interpolated model and update the flow by backpropagating the FWI data misfit, providing self-supervision without external training pairs. Experiments on challenging synthetic benchmarks show that SFM-FWI delivers more accurate reconstructions, greater noise robustness, and more stable convergence than standard FWI and pretraining-free regularization methods.

While score-based generative models have emerged as powerful priors for solving inverse problems, directly integrating them into optimization algorithms such as ADMM remains nontrivial. Two central challenges arise: i) the mismatch between the noisy data manifolds used to train the score functions and the geometry of ADMM iterates, especially due to the influence of dual variables, and ii) the lack of convergence understanding when ADMM is equipped with score-based denoisers. To address the manifold mismatch issue, we propose ADMM plug-and-play (ADMM-PnP) with the AC-DC denoiser, a new framework that embeds a three-stage denoiser into ADMM: (1) auto-correction (AC) via additive Gaussian noise, (2) directional correction (DC) using conditional Langevin dynamics, and (3) score-based denoising. In terms of convergence, we establish two results: first, under proper denoiser parameters, each ADMM iteration is a weakly nonexpansive operator, ensuring high-probability fixed-point $\textit{ball convergence}$ using a constant step size; second, under more relaxed conditions, the AC-DC denoiser is a bounded denoiser, which leads to convergence under an adaptive step size schedule. Experiments on a range of inverse problems demonstrate that our method consistently improves solution quality over a variety of baselines.

Scientific machine learning (SciML) is increasingly applied to in-field processing, controlling, and monitoring; however, wide-area sensing, real-time demands, and strict energy and reliability constraints make centralized SciML implementation impractical. Most SciML models assume raw data aggregation at a central node, incurring prohibitively high communication latency and energy costs; yet, distributing models developed for general-purpose ML often breaks essential physical principles, resulting in degraded performance. To address these challenges, we introduce EPIC, a hardware- and physics-co-guided distributed SciML framework, using full-waveform inversion (FWI) as a representative task. EPIC performs lightweight local encoding on end devices and physics-aware decoding at a central node. By transmitting compact latent features rather than high-volume raw data and by using cross-attention to capture inter-receiver wavefield coupling, EPIC significantly reduces communication cost while preserving physical fidelity. Evaluated on a distributed testbed with five end devices and one central node, and across 10 datasets from OpenFWI, EPIC reduces latency by 8.9$\times$ and communication energy by 33.8$\times$, while even improving reconstruction fidelity on 8 out of 10 datasets.

Latent generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals at a single, fixed complexity, governed by the latent dimensionality. This can be limiting: depending on the problem, a latent dimensionality that is too small may result in high representation error, while one that is too large may overfit to noise. We develop tunable latent priors for diffusion models, normalizing flows, and variational autoencoders, leveraging nested dropout. Across tasks including compressed sensing, inpainting, denoising, and phase retrieval, we show empirically that tunable priors consistently achieve lower reconstruction errors than fixed-complexity baselines. In the linear denoising setting, we derive the optimal complexity in closed form, showing how it depends on the noise level and the signal spectrum. This work demonstrates the potential of tunable latent generative priors and motivates both the development of supporting theory and their application across a wide range of inverse problems.

Subsurface ore detection is of paramount importance given the rising depletion of shallow mineral resources in recent years. It is crucial to explore approaches that go beyond the limitations of traditional geological exploration methods. Due to readily available surface readings, joint magnetic and gravitational inversion is a promising new method - given magnetic and gravitational data on a surface, jointly reconstructing the underlying densities that generate them. However, this is ill-posed and has non-unique solutions. Deterministic methods often require handcrafted priors and converge to a single solution and do not capture the distribution, which is often of interest. We introduce a novel framework that reframes 3D gravity and magnetic joint inversion as a rectified flow on the Noddyverse dataset, the largest physics-based dataset for inversion. We introduce a Ginzburg-Landau (GL) regularizer, a generalized version of the Ising model that aids in ore identification, enabling physics-aware training. We also propose a guidance methodology based on GL theory that can be used as a plug-and-play module with existing unconditional denoisers. Lastly, we also train and release a VAE for the 3D densities, which facilitates downstream work in the field.

We introduce the challenging problem of multi-object system identification from videos, for which prior methods are ill-suited due to their focus on single-object scenes or discrete material classification with a fixed set of material prototypes. To address this, we propose MOSIV, a new framework that directly optimizes for continuous, per-object material parameters using a differentiable simulator guided by geometric objectives derived from video. We also present a new synthetic benchmark with contact-rich, multi-object interactions to facilitate evaluation. On this benchmark, MOSIV substantially improves grounding accuracy and long-horizon simulation fidelity over adapted baselines, establishing it as a strong baseline for this new task. Our analysis shows that object-level fine-grained supervision and geometry-aligned objectives are critical for stable optimization in these complex, multi-object settings. The source code and dataset will be released.

State-of-the-art EfficientSCI loses 20.58 dB when its assumed forward operator deviates from physical reality in just eight parameters, yet no existing benchmark quantifies operator mismatch, the default condition in deployed compressive imaging systems. We introduce InverseNet, the first cross-modality benchmark for operator mismatch, spanning CASSI, CACTI, and single-pixel cameras. Evaluating 12 methods under a four-scenario protocol (ideal, mismatched, oracle-corrected, blind calibration) across 27 simulated scenes and 9 real hardware captures, we find: (1) deep learning methods lose 10-21 dB under mismatch, eliminating their advantage over classical baselines; (2) performance and robustness are inversely correlated across modalities (Spearman r_s = -0.71, p < 0.01); (3) mask-oblivious architectures recover 0% of mismatch losses regardless of calibration quality, while operator-conditioned methods recover 41-90%; (4) blind grid-search calibration recovers 85-100% of the oracle bound without ground truth. Real hardware experiments confirm that simulation trends transfer to physical data. Code will be released upon acceptance.