Daily Papers

Deep neural networks set the state-of-the-art across many tasks in computer vision, but their generalization ability to image distortions is surprisingly fragile. In contrast, the mammalian visual system is robust to a wide range of perturbations. Recent work suggests that this generalization ability can be explained by useful inductive biases encoded in the representations of visual stimuli throughout the visual cortex. Here, we successfully leveraged these inductive biases with a multi-task learning approach: we jointly trained a deep network to perform image classification and to predict neural activity in macaque primary visual cortex (V1). We measured the out-of-distribution generalization abilities of our network by testing its robustness to image distortions. We found that co-training on monkey V1 data leads to increased robustness despite the absence of those distortions during training. Additionally, we showed that our network's robustness is very close to that of an Oracle network where parts of the architecture are directly trained on noisy images. Our results also demonstrated that the network's representations become more brain-like as their robustness improves. Using a novel constrained reconstruction analysis, we investigated what makes our brain-regularized network more robust. We found that our co-trained network is more sensitive to content than noise when compared to a Baseline network that we trained for image classification alone. Using DeepGaze-predicted saliency maps for ImageNet images, we found that our monkey co-trained network tends to be more sensitive to salient regions in a scene, reminiscent of existing theories on the role of V1 in the detection of object borders and bottom-up saliency. Overall, our work expands the promising research avenue of transferring inductive biases from the brain, and provides a novel analysis of the effects of our transfer.

Large collections of matrices arise throughout modern machine learning, signal processing, and scientific computing, where they are commonly compressed by concatenation followed by truncated singular value decomposition (SVD). This strategy enables parameter sharing and efficient reconstruction and has been widely adopted across domains ranging from multi-view learning and signal processing to neural network compression. However, it leaves a fundamental question unanswered: which matrices can be safely concatenated and compressed together under explicit reconstruction error constraints? Existing approaches rely on heuristic or architecture-specific grouping and provide no principled guarantees on the resulting SVD approximation error. In the present work, we introduce a theory-driven framework for compression-aware clustering of matrices under SVD compression constraints. Our analysis establishes new spectral bounds for horizontally concatenated matrices, deriving global upper bounds on the optimal rank-r SVD reconstruction error from lower bounds on singular value growth. The first bound follows from Weyl-type monotonicity under blockwise extensions, while the second leverages singular values of incremental residuals to yield tighter, per-block guarantees. We further develop an efficient approximate estimator based on incremental truncated SVD that tracks dominant singular values without forming the full concatenated matrix. Therefore, we propose three clustering algorithms that merge matrices only when their predicted joint SVD compression error remains below a user-specified threshold. The algorithms span a trade-off between speed, provable accuracy, and scalability, enabling compression-aware clustering with explicit error control. Code is available online.

For non-rigid objects, predicting the 3D shape from 2D keypoint observations is ill-posed due to occlusions, and the need to disentangle changes in viewpoint and changes in shape. This challenge has often been addressed by embedding low-rank constraints into specialized models. These models can be hard to train, as they depend on finding a canonical way of aligning observations, before they can learn detailed geometry. These constraints have limited the reconstruction quality. We show that generic, high capacity models, trained with an unsupervised loss, allow for more accurate predicted shapes. In particular, applying low-rank constraints to localized subsets of the full shape allows the high capacity to be suitably constrained. We reduce the state-of-the-art reconstruction error on the S-Up3D dataset by over 70%.

Reconstructing 3D clothed humans from monocular images and videos is a fundamental problem with applications in virtual try-on, avatar creation, and mixed reality. Despite significant progress in human body recovery, accurately reconstructing garment geometry, particularly for loose-fitting clothing, remains an open challenge. We propose a unified framework for high-fidelity 3D garment reconstruction from both single images and video sequences. Our approach combines Implicit Sewing Patterns (ISP) with a generative diffusion model to learn expressive garment shape priors in 2D UV space. Leveraging these priors, we introduce a mapping model that establishes correspondences between image pixels, UV pattern coordinates, and 3D geometry, enabling accurate and detailed garment reconstruction from single images. We further extend this formulation to dynamic reconstruction by introducing a spatio-temporal diffusion scheme with test-time guidance to enforce long-range temporal consistency. We also develop analytic projection-based constraints that preserve image-aligned geometry in visible regions while enforcing coherent completion in occluded areas over time. Although trained exclusively on synthetically simulated cloth data, our method generalizes well to real-world imagery and consistently outperforms existing approaches on both tight- and loose-fitting garments. The reconstructed garments preserve fine geometric detail while exhibiting realistic dynamic motion, supporting downstream applications such as texture editing, garment retargeting, and animation.

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step followed by a projection-based measurement consistency step, often produce suboptimal results. By studying the generative sampling path, here we show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, we propose an additional correction term inspired by the manifold constraint, which can be used synergistically with the previous solvers to make the iterations close to the manifold. The proposed manifold constraint is straightforward to implement within a few lines of code, yet boosts the performance by a surprisingly large margin. With extensive experiments, we show that our method is superior to the previous methods both theoretically and empirically, producing promising results in many applications such as image inpainting, colorization, and sparse-view computed tomography. Code available https://github.com/HJ-harry/MCG_diffusion

Decompositional reconstruction of 3D scenes, with complete shapes and detailed texture of all objects within, is intriguing for downstream applications but remains challenging, particularly with sparse views as input. Recent approaches incorporate semantic or geometric regularization to address this issue, but they suffer significant degradation in underconstrained areas and fail to recover occluded regions. We argue that the key to solving this problem lies in supplementing missing information for these areas. To this end, we propose DP-Recon, which employs diffusion priors in the form of Score Distillation Sampling (SDS) to optimize the neural representation of each individual object under novel views. This provides additional information for the underconstrained areas, but directly incorporating diffusion prior raises potential conflicts between the reconstruction and generative guidance. Therefore, we further introduce a visibility-guided approach to dynamically adjust the per-pixel SDS loss weights. Together these components enhance both geometry and appearance recovery while remaining faithful to input images. Extensive experiments across Replica and ScanNet++ demonstrate that our method significantly outperforms SOTA methods. Notably, it achieves better object reconstruction under 10 views than the baselines under 100 views. Our method enables seamless text-based editing for geometry and appearance through SDS optimization and produces decomposed object meshes with detailed UV maps that support photorealistic Visual effects (VFX) editing. The project page is available at https://dp-recon.github.io/.

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its reconstruction error via connections to higher-order singular values. Specifically, we introduce a novel Tucker packing problem, which we prove is NP-hard, and give a polynomial-time approximation scheme based on a reduction to the 2-dimensional knapsack problem with a matroid constraint. We also generalize our techniques to tree tensor network decompositions. We implement our algorithm using an integer programming solver, and show that its solution quality is competitive with (and sometimes better than) the greedy algorithm that uses the true Tucker decomposition loss at each step, while also running up to 1000x faster.

Geographical, physical, or economic constraints often result in missing traces within seismic data, making the reconstruction of complete seismic data a crucial step in seismic data processing. Traditional methods for seismic data reconstruction require the selection of multiple empirical parameters and struggle to handle large-scale continuous missing data. With the development of deep learning, various neural networks have demonstrated powerful reconstruction capabilities. However, these convolutional neural networks represent a point-to-point reconstruction approach that may not cover the entire distribution of the dataset. Consequently, when dealing with seismic data featuring complex missing patterns, such networks may experience varying degrees of performance degradation. In response to this challenge, we propose a novel diffusion model reconstruction framework tailored for 3D seismic data. To constrain the results generated by the diffusion model, we introduce conditional supervision constraints into the diffusion model, constraining the generated data of the diffusion model based on the input data to be reconstructed. We introduce a 3D neural network architecture into the diffusion model, successfully extending the 2D diffusion model to 3D space. Additionally, we refine the model's generation process by incorporating missing data into the generation process, resulting in reconstructions with higher consistency. Through ablation studies determining optimal parameter values, our method exhibits superior reconstruction accuracy when applied to both field datasets and synthetic datasets, effectively addressing a wide range of complex missing patterns. Our implementation is available at https://github.com/WAL-l/SeisFusion.

The inherent generative power of denoising diffusion models makes them well-suited for image restoration tasks where the objective is to find the optimal high-quality image within the generative space that closely resembles the input image. We propose a method to adapt a pretrained diffusion model for image restoration by simply adding noise to the input image to be restored and then denoise. Our method is based on the observation that the space of a generative model needs to be constrained. We impose this constraint by finetuning the generative model with a set of anchor images that capture the characteristics of the input image. With the constrained space, we can then leverage the sampling strategy used for generation to do image restoration. We evaluate against previous methods and show superior performances on multiple real-world restoration datasets in preserving identity and image quality. We also demonstrate an important and practical application on personalized restoration, where we use a personal album as the anchor images to constrain the generative space. This approach allows us to produce results that accurately preserve high-frequency details, which previous works are unable to do. Project webpage: https://gen2res.github.io.

Arbitrary slice super-resolution reconstructs isotropic volumes from anisotropic clinical acquisitions by synthesizing intermediate slices at arbitrary scales. However, treating this ill-posed inverse problem as unconstrained residual-based regression risks hallucinating anatomically implausible structures or altering the originally observed data. To address both concerns, this paper presents the Dual-Prior Null-space Learning (DP-NSL) framework, which reformulates the task as a constrained recovery process guided by two complementary priors. A Measurement-Consistent Projection (MCP) enforces a Deterministic Observation Prior: the reconstruction undergoes an exact orthogonal projection that reproduces every acquired slice with zero error, confining all learned details to the unobservable null space. Within this null space, a Mixture-of-Splines (MoS) module imposes a Geometric Continuity Prior by dynamically mixing B-spline experts of different analytic orders, allowing each anatomical region to be modeled with a content-aware level of continuity. To promote spatial coherence, a Local Spatial Consistency Decoder (LSCD) further injects local inductive bias. Experiments on three CT and one MRI benchmark show that DP-NSL outperforms existing approaches while strictly preserving measurement consistency. Code is available at https://github.com/DeepMed-Lab-ECNU/Medical-Image-Reconstruction.

The rate-distortion-perception (RDP) trade-off extends classical rate--distortion theory by imposing a distributional constraint on reconstructions, providing a unified framework for neural image compression that jointly governs fidelity and perceptual realism. While prior work achieves near-optimal rate--perception trade-offs, practical frameworks explicitly realizing the full RDP surface remain scarce, primarily due to the difficulty of introducing common randomness at the decoder. We propose DCIC (Dual-Constrained Diffusion Image Compression), which integrates a learned codec with a diffusion-based decoder governed by joint distortion and idempotence constraints. The distortion constraint bounds reconstruction fidelity relative to the base codec output; the idempotence constraint -- requiring that re-encoding the restored image recovers the base codec reconstruction -- serves as a tractable surrogate for the distributional perception requirement. Together, they steer the reverse denoising process via iterative optimization with consistent noise injection, realizing common randomness without additional rate overhead. At fixed rate, dual attenuation factors (K_D, K_P) jointly navigate the Pareto frontier of the distortion-perception plane, enabling continuously adjustable fidelity-realism trade-offs from a single bitstream. DCIC_{RD} (K_P{=}0) and DCIC_{RP} (K_D{=}0) arise as boundary curves, with DCIC_{RDP} (K_D = K_P=1) realizing the optimal interior operating point. Experiments on CelebA-HQ, CLIC2020, and ImageNet-1K across CNN, Transformer, and hybrid architectures confirm that DCIC_{RDP} achieves superior BD-PSNR over all perceptual codecs, while DCIC_{RP} matches dedicated perception-oriented methods in BD-FID, validating the practical value of full RDP surface navigation.

3D reconstruction methods such as Neural Radiance Fields (NeRFs) excel at rendering photorealistic novel views of complex scenes. However, recovering a high-quality NeRF typically requires tens to hundreds of input images, resulting in a time-consuming capture process. We present ReconFusion to reconstruct real-world scenes using only a few photos. Our approach leverages a diffusion prior for novel view synthesis, trained on synthetic and multiview datasets, which regularizes a NeRF-based 3D reconstruction pipeline at novel camera poses beyond those captured by the set of input images. Our method synthesizes realistic geometry and texture in underconstrained regions while preserving the appearance of observed regions. We perform an extensive evaluation across various real-world datasets, including forward-facing and 360-degree scenes, demonstrating significant performance improvements over previous few-view NeRF reconstruction approaches.

What do auto-encoders learn about the underlying data generating distribution? Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of data. This paper clarifies some of these previous observations by showing that minimizing a particular form of regularized reconstruction error yields a reconstruction function that locally characterizes the shape of the data generating density. We show that the auto-encoder captures the score (derivative of the log-density with respect to the input). It contradicts previous interpretations of reconstruction error as an energy function. Unlike previous results, the theorems provided here are completely generic and do not depend on the parametrization of the auto-encoder: they show what the auto-encoder would tend to if given enough capacity and examples. These results are for a contractive training criterion we show to be similar to the denoising auto-encoder training criterion with small corruption noise, but with contraction applied on the whole reconstruction function rather than just encoder. Similarly to score matching, one can consider the proposed training criterion as a convenient alternative to maximum likelihood because it does not involve a partition function. Finally, we show how an approximate Metropolis-Hastings MCMC can be setup to recover samples from the estimated distribution, and this is confirmed in sampling experiments.

We present a novel approach to mesh shape editing, building on recent progress in 3D reconstruction from multi-view images. We formulate shape editing as a conditional reconstruction problem, where the model must reconstruct the input shape with the exception of a specified 3D region, in which the geometry should be generated from the conditional signal. To this end, we train a conditional Large Reconstruction Model (LRM) for masked reconstruction, using multi-view consistent masks rendered from a randomly generated 3D occlusion, and using one clean viewpoint as the conditional signal. During inference, we manually define a 3D region to edit and provide an edited image from a canonical viewpoint to fill in that region. We demonstrate that, in just a single forward pass, our method not only preserves the input geometry in the unmasked region through reconstruction capabilities on par with SoTA, but is also expressive enough to perform a variety of mesh edits from a single image guidance that past works struggle with, while being 10x faster than the top-performing competing prior work.

The field of 3D reconstruction from images has rapidly evolved in the past few years, first with the introduction of Neural Radiance Field (NeRF) and more recently with 3D Gaussian Splatting (3DGS). The latter provides a significant edge over NeRF in terms of the training and inference speed, as well as the reconstruction quality. Although 3DGS works well for dense input images, the unstructured point-cloud like representation quickly overfits to the more challenging setup of extremely sparse input images (e.g., 3 images), creating a representation that appears as a jumble of needles from novel views. To address this issue, we propose regularized optimization and depth-based initialization. Our key idea is to introduce a structured Gaussian representation that can be controlled in 2D image space. We then constraint the Gaussians, in particular their position, and prevent them from moving independently during optimization. Specifically, we introduce single and multiview constraints through an implicit convolutional decoder and a total variation loss, respectively. With the coherency introduced to the Gaussians, we further constrain the optimization through a flow-based loss function. To support our regularized optimization, we propose an approach to initialize the Gaussians using monocular depth estimates at each input view. We demonstrate significant improvements compared to the state-of-the-art sparse-view NeRF-based approaches on a variety of scenes.

We present an algorithm for reconstructing dense, geometrically consistent depth for all pixels in a monocular video. We leverage a conventional structure-from-motion reconstruction to establish geometric constraints on pixels in the video. Unlike the ad-hoc priors in classical reconstruction, we use a learning-based prior, i.e., a convolutional neural network trained for single-image depth estimation. At test time, we fine-tune this network to satisfy the geometric constraints of a particular input video, while retaining its ability to synthesize plausible depth details in parts of the video that are less constrained. We show through quantitative validation that our method achieves higher accuracy and a higher degree of geometric consistency than previous monocular reconstruction methods. Visually, our results appear more stable. Our algorithm is able to handle challenging hand-held captured input videos with a moderate degree of dynamic motion. The improved quality of the reconstruction enables several applications, such as scene reconstruction and advanced video-based visual effects.

3D Reconstruction of moving articulated objects without additional information about object structure is a challenging problem. Current methods overcome such challenges by employing category-specific skeletal models. Consequently, they do not generalize well to articulated objects in the wild. We treat an articulated object as an unknown, semi-rigid skeletal structure surrounded by nonrigid material (e.g., skin). Our method simultaneously estimates the visible (explicit) representation (3D shapes, colors, camera parameters) and the implicit skeletal representation, from motion cues in the object video without 3D supervision. Our implicit representation consists of four parts. (1) Skeleton, which specifies how semi-rigid parts are connected. (2) black{Skinning Weights}, which associates each surface vertex with semi-rigid parts with probability. (3) Rigidity Coefficients, specifying the articulation of the local surface. (4) Time-Varying Transformations, which specify the skeletal motion and surface deformation parameters. We introduce an algorithm that uses physical constraints as regularization terms and iteratively estimates both implicit and explicit representations. Our method is category-agnostic, thus eliminating the need for category-specific skeletons, we show that our method outperforms state-of-the-art across standard video datasets.

Recent advances in 3D reconstruction have achieved remarkable progress in high-quality scene capture from dense multi-view imagery, yet struggle when input views are limited. Various approaches, including regularization techniques, semantic priors, and geometric constraints, have been implemented to address this challenge. Latest diffusion-based methods have demonstrated substantial improvements by generating novel views from new camera poses to augment training data, surpassing earlier regularization and prior-based techniques. Despite this progress, we identify three critical limitations in these state-of-the-art approaches: inadequate coverage beyond known view peripheries, geometric inconsistencies across generated views, and computationally expensive pipelines. We introduce GaMO (Geometry-aware Multi-view Outpainter), a framework that reformulates sparse-view reconstruction through multi-view outpainting. Instead of generating new viewpoints, GaMO expands the field of view from existing camera poses, which inherently preserves geometric consistency while providing broader scene coverage. Our approach employs multi-view conditioning and geometry-aware denoising strategies in a zero-shot manner without training. Extensive experiments on Replica and ScanNet++ demonstrate state-of-the-art reconstruction quality across 3, 6, and 9 input views, outperforming prior methods in PSNR and LPIPS, while achieving a 25times speedup over SOTA diffusion-based methods with processing time under 10 minutes. Project page: https://yichuanh.github.io/GaMO/

This paper addresses the challenge of reconstructing 3D indoor scenes from multi-view images. Many previous works have shown impressive reconstruction results on textured objects, but they still have difficulty in handling low-textured planar regions, which are common in indoor scenes. An approach to solving this issue is to incorporate planer constraints into the depth map estimation in multi-view stereo-based methods, but the per-view plane estimation and depth optimization lack both efficiency and multi-view consistency. In this work, we show that the planar constraints can be conveniently integrated into the recent implicit neural representation-based reconstruction methods. Specifically, we use an MLP network to represent the signed distance function as the scene geometry. Based on the Manhattan-world assumption, planar constraints are employed to regularize the geometry in floor and wall regions predicted by a 2D semantic segmentation network. To resolve the inaccurate segmentation, we encode the semantics of 3D points with another MLP and design a novel loss that jointly optimizes the scene geometry and semantics in 3D space. Experiments on ScanNet and 7-Scenes datasets show that the proposed method outperforms previous methods by a large margin on 3D reconstruction quality. The code is available at https://zju3dv.github.io/manhattan_sdf.

Sparse-view computed tomography (CT) reduces radiation dose and acquisition time and may mitigate motion artifacts. However, angular undersampling provides insufficient information to determine the image uniquely and stably. Limited-angle CT, arising from restricted angular coverage, produces strongly directional information loss associated with the missing angular range. In both settings, image directions may be strongly observed, weakly constrained, or unobservable, leading to severe ill-posedness and reconstruction ambiguity. Existing diffusion-based approaches incorporate measurement information through likelihood guidance, data-consistency operations, or range-null-space corrections. However, they do not generally use the continuously varying measurement sensitivity of the acquisition to jointly shape both reconstruction updates and stochastic exploration. We propose a geometry-aware diffusion-guided stochastic reconstruction framework for sparse-view and limited-angle CT. Its central component is a regularized noise-weighted pullback metric constructed from the CT forward operator and measurement-noise covariance. This metric continuously adapts both the measurement-aware update and stochastic exploration according to directional measurement sensitivity, suppressing changes along strongly constrained directions while permitting greater exploration along weakly constrained and unobservable directions. We complement this geometry-aware update with a regularized data-consistency correction and approximately null-space-restricted stochastic perturbations, implemented matrix-free using forward and backprojection operations together with conjugate-gradient solves. Experiments on sparse-view, noisy, and limited-angle CT demonstrate competitive reconstruction quality, strong measurement consistency, and spatially resolved empirical uncertainty estimates.

Using Quadrics as the object representation has the benefits of both generality and closed-form projection derivation between image and world spaces. Although numerous constraints have been proposed for dual quadric reconstruction, we found that many of them are imprecise and provide minimal improvements to localization.After scrutinizing the existing constraints, we introduce a concise yet more precise convex hull-based algebraic constraint for object landmarks, which is applied to object reconstruction, frontend pose estimation, and backend bundle adjustment.This constraint is designed to fully leverage precise semantic segmentation, effectively mitigating mismatches between complex-shaped object contours and dual quadrics.Experiments on public datasets demonstrate that our approach is applicable to both monocular and RGB-D SLAM and achieves improved object mapping and localization than existing quadric SLAM methods. The implementation of our method is available at https://github.com/tiev-tongji/convexhull-based-algebraic-constraint.

Relightable object acquisition is a key challenge in simplifying digital asset creation. Complete reconstruction of an object typically requires capturing hundreds to thousands of photographs under controlled illumination, with specialized equipment. The recent progress in differentiable rendering improved the quality and accessibility of inverse rendering optimization. Nevertheless, under uncontrolled illumination and unstructured viewpoints, there is no guarantee that the observations contain enough information to reconstruct the appearance properties of the captured object. We thus propose to consider the acquisition process from a signal-processing perspective. Given an object's geometry and a lighting environment, we estimate the properties of the materials on the object's surface in seconds. We do so by leveraging frequency domain analysis, considering the recovery of material properties as a deconvolution, enabling fast error estimation. We then quantify the uncertainty of the estimation, based on the available data, highlighting the areas for which priors or additional samples would be required for improved acquisition quality. We compare our approach to previous work and quantitatively evaluate our results, showing similar quality as previous work in a fraction of the time, and providing key information about the certainty of the results.

Surface reconstruction from sparse views aims to reconstruct a 3D shape or scene from few RGB images. The latest methods are either generalization-based or overfitting-based. However, the generalization-based methods do not generalize well on views that were unseen during training, while the reconstruction quality of overfitting-based methods is still limited by the limited geometry clues. To address this issue, we propose SparseRecon, a novel neural implicit reconstruction method for sparse views with volume rendering-based feature consistency and uncertainty-guided depth constraint. Firstly, we introduce a feature consistency loss across views to constrain the neural implicit field. This design alleviates the ambiguity caused by insufficient consistency information of views and ensures completeness and smoothness in the reconstruction results. Secondly, we employ an uncertainty-guided depth constraint to back up the feature consistency loss in areas with occlusion and insignificant features, which recovers geometry details for better reconstruction quality. Experimental results demonstrate that our method outperforms the state-of-the-art methods, which can produce high-quality geometry with sparse-view input, especially in the scenarios with small overlapping views. Project page: https://hanl2010.github.io/SparseRecon/.

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

This paper describes an efficient algorithm for solving noisy linear inverse problems using pretrained diffusion models. Extending the paradigm of denoising diffusion implicit models (DDIM), we propose constrained diffusion implicit models (CDIM) that modify the diffusion updates to enforce a constraint upon the final output. For noiseless inverse problems, CDIM exactly satisfies the constraints; in the noisy case, we generalize CDIM to satisfy an exact constraint on the residual distribution of the noise. Experiments across a variety of tasks and metrics show strong performance of CDIM, with analogous inference acceleration to unconstrained DDIM: 10 to 50 times faster than previous conditional diffusion methods. We demonstrate the versatility of our approach on many problems including super-resolution, denoising, inpainting, deblurring, and 3D point cloud reconstruction.

This work addresses the problem of recovering complete, simulatable object geometry from reconstructed real-world scenes, enabling physics-based interaction with objects embedded in the scene. While modern multi-view reconstruction methods can produce visually accurate environments, objects are often incomplete due to occlusions and limited observations, making them unsuitable for physics simulation. To address this limitation, we propose SAM3D-Phys, a framework that integrates scene reconstruction with generative 3D priors of SAM3D to recover physically simulatable objects. Our approach first reconstructs the scene from multi-view images to obtain scene geometry and partial observations of objects. We then leverage SAM3D to infer complete object geometry from these partial observations. To ensure that the recovered objects remain consistent with the reconstructed scene, we restore scene-consistent object states through two complementary strategies: a physics-constrained spatial optimization algorithm that iteratively aligns the recovered object to its original location, and a mask-guided appearance distillation module that refines texture fidelity based on the observed images. By recovering complete object geometry and restoring its pose and appearance within the scene, SAM3D-Phys produces clean object representations suitable for physics-based simulation, enabling simultaneous and physically consistent interactive simulation of multiple objects within a reconstructed scene. Project page: https://chnxindong.github.io/sam3d-phys/

This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate approximation of the true image (or its gradient magnitude) through a neural network. Our approach operates without requiring prior knowledge of the noise intensity in the data and avoids the iterative recomputation of weights. Additionally, the paper includes a theoretical analysis of the proposed method, establishing its validity as a regularization approach. This framework integrates advanced neural network capabilities within a regularization context, thereby making the results of the networks interpretable. The results are promising as they enable high-quality reconstructions from limited-view tomographic measurements.

Reconstructing 3D shapes from planar cross-sections is a challenge inspired by downstream applications like medical imaging and geographic informatics. The input is an in/out indicator function fully defined on a sparse collection of planes in space, and the output is an interpolation of the indicator function to the entire volume. Previous works addressing this sparse and ill-posed problem either produce low quality results, or rely on additional priors such as target topology, appearance information, or input normal directions. In this paper, we present OReX, a method for 3D shape reconstruction from slices alone, featuring a Neural Field as the interpolation prior. A modest neural network is trained on the input planes to return an inside/outside estimate for a given 3D coordinate, yielding a powerful prior that induces smoothness and self-similarities. The main challenge for this approach is high-frequency details, as the neural prior is overly smoothing. To alleviate this, we offer an iterative estimation architecture and a hierarchical input sampling scheme that encourage coarse-to-fine training, allowing the training process to focus on high frequencies at later stages. In addition, we identify and analyze a ripple-like effect stemming from the mesh extraction step. We mitigate it by regularizing the spatial gradients of the indicator function around input in/out boundaries during network training, tackling the problem at the root. Through extensive qualitative and quantitative experimentation, we demonstrate our method is robust, accurate, and scales well with the size of the input. We report state-of-the-art results compared to previous approaches and recent potential solutions, and demonstrate the benefit of our individual contributions through analysis and ablation studies.

The denoising process of diffusion models can be interpreted as an approximate projection of noisy samples onto the data manifold. Moreover, the noise level in these samples approximates their distance to the underlying manifold. Building on this insight, we propose a novel method to enhance sample generation by aligning the estimated noise level with the true distance of noisy samples to the manifold. Specifically, we introduce a noise level correction network, leveraging a pre-trained denoising network, to refine noise level estimates during the denoising process. Additionally, we extend this approach to various image restoration tasks by integrating task-specific constraints, including inpainting, deblurring, super-resolution, colorization, and compressed sensing. Experimental results demonstrate that our method significantly improves sample quality in both unconstrained and constrained generation scenarios. Notably, the proposed noise level correction framework is compatible with existing denoising schedulers (e.g., DDIM), offering additional performance improvements.

While highly accelerated non-Cartesian acquisition protocols significantly reduce scan time, they often entail long reconstruction delays. Deep learning based reconstruction methods can alleviate this, but often lack stability and robustness to distribution shifts. As an alternative, we train a rotation invariant weakly convex ridge regularizer (WCRR). The resulting variational reconstruction approach is benchmarked against state of the art methods on retrospectively simulated data and (out of distribution) on prospective GoLF SPARKLING and CAIPIRINHA acquisitions. Our approach consistently outperforms widely used baselines and achieves performance comparable to Plug and Play reconstruction with a state of the art 3D DRUNet denoiser, while offering substantially improved computational efficiency and robustness to acquisition changes. In summary, WCRR unifies the strengths of principled variational methods and modern deep learning based approaches.

Recent feed-forward geometry foundation models have demonstrated impressive generalization by recovering depth and poses in a single forward pass. However, these models are typically constrained by a global coordinate frame assumption. This dependency becomes a significant bottleneck for long-context and streaming reconstruction, as it forces the network to maintain an arbitrary temporal origin and handle translation magnitudes that grow unbounded over time. Our solution, which we call R^3, employs relative regression. We employ a lightweight MLP to predict confidence-weighted relative constraints. These confidences serve as a unified anchor: weighting losses during training and guiding pose aggregation during inference. R^3 supports both full-context offline reconstruction and causal, bounded-memory streaming. Our evaluation in both offline and streaming settings validates the effectiveness of our relative mechanism. Project page: https://kevinxu02.github.io/r3-site

We propose a method to estimate 3D human poses from substantially blurred images. The key idea is to tackle the inverse problem of image deblurring by modeling the forward problem with a 3D human model, a texture map, and a sequence of poses to describe human motion. The blurring process is then modeled by a temporal image aggregation step. Using a differentiable renderer, we can solve the inverse problem by backpropagating the pixel-wise reprojection error to recover the best human motion representation that explains a single or multiple input images. Since the image reconstruction loss alone is insufficient, we present additional regularization terms. To the best of our knowledge, we present the first method to tackle this problem. Our method consistently outperforms other methods on significantly blurry inputs since they lack one or multiple key functionalities that our method unifies, i.e. image deblurring with sub-frame accuracy and explicit 3D modeling of non-rigid human motion.

Reconstruction-based unsupervised learning can fail in two opposing ways: a model may reconstruct anomalies too accurately or discard valid nominal variation. Using the Pursuit of Subspaces hypothesis, we characterize these failures through the meet, union, and join geometries induced by the nominal components. Excess learned range produces join blindness, while insufficient capacity produces meet preference and loss of nominal fidelity. We show that the compact nominal union is optimal among nominal faithful ranges and generally requires a nonlinear reconstruction map. Based on this geometry, we introduce Dynamic Push and Pull, which learns from controlled perturbations without anomaly labels, and nested manifold carving, which applies the same principle recursively in latent space. Experiments confirm the predicted changes in latent geometry across every tested Push and Pull configuration. The proposed methods improve reconstruction-based anomaly detection across standard benchmarks and unseen image degradations, while also improving pretrained ECG representations for downstream classification. These results connect reconstruction failures to identifiable geometric conditions and provide practical mechanisms for learning compact representations.

Many modern iterative solvers for large-scale tomographic reconstruction incur two major computational costs per iteration: expensive forward/adjoint projections to update the data fidelity term and costly proximal computations for the regulariser, often done via inner iterations. This paper studies for the first time the application of methods that couple randomised skipping of the proximal with variance-reduced subset-based optimisation of data-fit term, to simultaneously reduce both costs in challenging tomographic reconstruction tasks. We provide a series of experiments using both synthetic and real data, demonstrating striking speed-ups of the order 5x--20x compared to the non-skipped counterparts which have been so far the standard approach for efficiently solving these problems. Our work lays the groundwork for broader adoption of these methods in inverse problems.

The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise model. As a result, accurate reconstruction of a spatially or temporally distributed phenomenon (f*) from Poisson data (y) cannot be effectively accomplished by minimizing a conventional penalized least-squares objective function. The problem addressed in this paper is the estimation of f* from y in an inverse problem setting, where (a) the number of unknowns may potentially be larger than the number of observations and (b) f* admits a sparse approximation. The optimization formulation considered in this paper uses a penalized negative Poisson log-likelihood objective function with nonnegativity constraints (since Poisson intensities are naturally nonnegative). In particular, the proposed approach incorporates key ideas of using separable quadratic approximations to the objective function at each iteration and penalization terms related to l1 norms of coefficient vectors, total variation seminorms, and partition-based multiscale estimation methods.

Reconstructing dynamic assets from video data is central to many in computer vision and graphics tasks. Existing 4D reconstruction approaches are limited by category-specific models or slow optimization-based methods. Inspired by the recent Large Reconstruction Model (LRM), we present the Large Interpolation Model (LIM), a transformer-based feed-forward solution, guided by a novel causal consistency loss, for interpolating implicit 3D representations across time. Given implicit 3D representations at times t_0 and t_1, LIM produces a deformed shape at any continuous time tin[t_0,t_1], delivering high-quality interpolated frames in seconds. Furthermore, LIM allows explicit mesh tracking across time, producing a consistently uv-textured mesh sequence ready for integration into existing production pipelines. We also use LIM, in conjunction with a diffusion-based multiview generator, to produce dynamic 4D reconstructions from monocular videos. We evaluate LIM on various dynamic datasets, benchmarking against image-space interpolation methods (e.g., FiLM) and direct triplane linear interpolation, and demonstrate clear advantages. In summary, LIM is the first feed-forward model capable of high-speed tracked 4D asset reconstruction across diverse categories.

We aim to address sparse-view reconstruction of a 3D scene by leveraging priors from large-scale vision models. While recent advancements such as 3D Gaussian Splatting (3DGS) have demonstrated remarkable successes in 3D reconstruction, these methods typically necessitate hundreds of input images that densely capture the underlying scene, making them time-consuming and impractical for real-world applications. However, sparse-view reconstruction is inherently ill-posed and under-constrained, often resulting in inferior and incomplete outcomes. This is due to issues such as failed initialization, overfitting on input images, and a lack of details. To mitigate these challenges, we introduce LM-Gaussian, a method capable of generating high-quality reconstructions from a limited number of images. Specifically, we propose a robust initialization module that leverages stereo priors to aid in the recovery of camera poses and the reliable point clouds. Additionally, a diffusion-based refinement is iteratively applied to incorporate image diffusion priors into the Gaussian optimization process to preserve intricate scene details. Finally, we utilize video diffusion priors to further enhance the rendered images for realistic visual effects. Overall, our approach significantly reduces the data acquisition requirements compared to previous 3DGS methods. We validate the effectiveness of our framework through experiments on various public datasets, demonstrating its potential for high-quality 360-degree scene reconstruction. Visual results are on our website.

Model pruning is a popular approach to enable the deployment of large deep learning models on edge devices with restricted computational or storage capacities. Although sparse models achieve performance comparable to that of their dense counterparts at the level of the entire dataset, they exhibit high accuracy drops for some data sub-groups. Existing methods to mitigate this disparate impact induced by pruning (i) rely on surrogate metrics that address the problem indirectly and have limited interpretability; or (ii) scale poorly with the number of protected sub-groups in terms of computational cost. We propose a constrained optimization approach that directly addresses the disparate impact of pruning: our formulation bounds the accuracy change between the dense and sparse models, for each sub-group. This choice of constraints provides an interpretable success criterion to determine if a pruned model achieves acceptable disparity levels. Experimental results demonstrate that our technique scales reliably to problems involving large models and hundreds of protected sub-groups.

Recent advances in radiance fields and novel view synthesis enable creation of realistic digital twins from photographs. However, current methods struggle with flat, texture-less surfaces, creating uneven and semi-transparent reconstructions, due to an ill-conditioned photometric reconstruction objective. Surface reconstruction methods solve this issue but sacrifice visual quality. We propose a novel hybrid 2D/3D representation that jointly optimizes constrained planar (2D) Gaussians for modeling flat surfaces and freeform (3D) Gaussians for the rest of the scene. Our end-to-end approach dynamically detects and refines planar regions, improving both visual fidelity and geometric accuracy. It achieves state-of-the-art depth estimation on ScanNet++ and ScanNetv2, and excels at mesh extraction without overfitting to a specific camera model, showing its effectiveness in producing high-quality reconstruction of indoor scenes.

Recent studies suggest that diffusion models can recover geometric structure in the data manifolds they are trained on, yet the supporting evidence has so far come mostly from natural-image data, where the underlying geometry itself is unknown. We study this question in a setting where the geometry is analytically tractable: constrained inverse kinematics (IK). Each task-space constraint defines a configuration-space manifold with known intrinsic dimension, giving direct ground truth for evaluating the geometry learned by the model. For each of the 6-DoF UR5 and 7-DoF Franka, we train a single conditional diffusion model across seven constraint families, spanning solution manifolds from discrete IK branches to self-motion manifolds. Our empirical results reveal that the intrinsic dimension recovered from the model's score function matches the analytical degrees of freedom of the corresponding constraint manifold across both robots. Moreover, linear interpolation in the latent space leads to generated solutions that remain close to the appropriate constraint manifold, indicating that the learned representation further captures geometric structure of the constraint family beyond intrinsic dimension alone. Constrained IK therefore offers a controlled setting for studying the intrinsic geometry learned by diffusion models.

Diffusion inversion is the problem of taking an image and a text prompt that describes it and finding a noise latent that would generate the image. Most current inversion techniques operate by approximately solving an implicit equation and may converge slowly or yield poor reconstructed images. Here, we formulate the problem as finding the roots of an implicit equation and design a method to solve it efficiently. Our solution is based on Newton-Raphson (NR), a well-known technique in numerical analysis. A naive application of NR may be computationally infeasible and tends to converge to incorrect solutions. We describe an efficient regularized formulation that converges quickly to a solution that provides high-quality reconstructions. We also identify a source of inconsistency stemming from prompt conditioning during the inversion process, which significantly degrades the inversion quality. To address this, we introduce a prompt-aware adjustment of the encoding, effectively correcting this issue. Our solution, Regularized Newton-Raphson Inversion, inverts an image within 0.5 sec for latent consistency models, opening the door for interactive image editing. We further demonstrate improved results in image interpolation and generation of rare objects.

Accurate reconstruction of both the geometric and topological details of a 3D object from a single 2D image embodies a fundamental challenge in computer vision. Existing explicit/implicit solutions to this problem struggle to recover self-occluded geometry and/or faithfully reconstruct topological shape structures. To resolve this dilemma, we introduce LIST, a novel neural architecture that leverages local and global image features to accurately reconstruct the geometric and topological structure of a 3D object from a single image. We utilize global 2D features to predict a coarse shape of the target object and then use it as a base for higher-resolution reconstruction. By leveraging both local 2D features from the image and 3D features from the coarse prediction, we can predict the signed distance between an arbitrary point and the target surface via an implicit predictor with great accuracy. Furthermore, our model does not require camera estimation or pixel alignment. It provides an uninfluenced reconstruction from the input-view direction. Through qualitative and quantitative analysis, we show the superiority of our model in reconstructing 3D objects from both synthetic and real-world images against the state of the art.

This report describes the solution that secured the first place in the "View Synthesis Challenge for Human Heads (VSCHH)" at the ICCV 2023 workshop. Given the sparse view images of human heads, the objective of this challenge is to synthesize images from novel viewpoints. Due to the complexity of textures on the face and the impact of lighting, the baseline method TensoRF yields results with significant artifacts, seriously affecting facial reconstruction. To address this issue, we propose TI-Face, which improves facial reconstruction through tensorial radiance fields (T-Face) and implicit surfaces (I-Face), respectively. Specifically, we employ an SAM-based approach to obtain the foreground mask, thereby filtering out intense lighting in the background. Additionally, we design mask-based constraints and sparsity constraints to eliminate rendering artifacts effectively. The experimental results demonstrate the effectiveness of the proposed improvements and superior performance of our method on face reconstruction. The code will be available at https://github.com/RuijieZhu94/TI-Face.

Sparse-view 3D CT reconstruction aims to recover volumetric structures from a limited number of 2D X-ray projections. Existing feedforward methods are constrained by the scarcity of large-scale training datasets and the absence of direct and consistent 3D representations. In this paper, we propose an X-ray Large Reconstruction Model (X-LRM) for extremely sparse-view (<10 views) CT reconstruction. X-LRM consists of two key components: X-former and X-triplane. X-former can handle an arbitrary number of input views using an MLP-based image tokenizer and a Transformer-based encoder. The output tokens are then upsampled into our X-triplane representation, which models the 3D radiodensity as an implicit neural field. To support the training of X-LRM, we introduce Torso-16K, a large-scale dataset comprising over 16K volume-projection pairs of various torso organs. Extensive experiments demonstrate that X-LRM outperforms the state-of-the-art method by 1.5 dB and achieves 27times faster speed with better flexibility. Furthermore, the evaluation of lung segmentation tasks also suggests the practical value of our approach. Our code and dataset will be released at https://github.com/Richard-Guofeng-Zhang/X-LRM

Sparse-view 3D scene reconstruction with 3D Gaussian Splatting (3DGS) is inherently underconstrained. Plausible renderings can also coexist with erroneous Gaussian geometry, as errors in positions or depths may be concealed by opacity, scale, and appearance; we term this failure mode Geometry Cheating. Existing regularization methods constrain geometry but remain limited to observed views, while video-diffusion-based methods complete unseen views yet mainly use them as RGB pseudo-supervision, underusing motion and temporal priors and lacking explicit geometry supervision. We present Bi-FlowGS, which uses optical flow to bridge generative view completion and Gaussian geometry regularization. Our plug-and-play Video-to-Geometry Flow Distillation (V2G) distills temporal correspondence priors from restored videos into Gaussian geometry to alleviate Geometry Cheating. Conversely, Geometry-to-Video Flow-Guided Restoration (G2V) uses the current 3DGS geometry to guide temporally consistent video restoration, providing more reliable generative supervision. Together, V2G and G2V form an implicit bidirectional co-refinement process, enabling restored videos and the optimized 3DGS scene to iteratively improve each other. Experiments demonstrate improved rendering quality and geometric consistency across wide-baseline and unbounded 360° benchmarks.

Reconstructing dynamic objects from monocular videos is a severely underconstrained and challenging problem, and recent work has approached it in various directions. However, owing to the ill-posed nature of this problem, there has been no solution that can provide consistent, high-quality novel views from camera positions that are significantly different from the training views. In this work, we introduce Neural Parametric Gaussians (NPGs) to take on this challenge by imposing a two-stage approach: first, we fit a low-rank neural deformation model, which then is used as regularization for non-rigid reconstruction in the second stage. The first stage learns the object's deformations such that it preserves consistency in novel views. The second stage obtains high reconstruction quality by optimizing 3D Gaussians that are driven by the coarse model. To this end, we introduce a local 3D Gaussian representation, where temporally shared Gaussians are anchored in and deformed by local oriented volumes. The resulting combined model can be rendered as radiance fields, resulting in high-quality photo-realistic reconstructions of the non-rigidly deforming objects, maintaining 3D consistency across novel views. We demonstrate that NPGs achieve superior results compared to previous works, especially in challenging scenarios with few multi-view cues.

We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our algorithm showing provable sample recovery in a linear model setting. The algorithmic insight obtained from our analysis extends to more general settings often considered in practice. Experimentally, we outperform previously proposed posterior sampling algorithms in a wide variety of problems including random inpainting, block inpainting, denoising, deblurring, destriping, and super-resolution.

Diffusion models are the current state of the art for generating photorealistic images. Controlling the sampling process for constrained image generation tasks such as inpainting, however, remains challenging since exact conditioning on such constraints is intractable. While existing methods use various techniques to approximate the constrained posterior, this paper proposes to exploit the ability of Tractable Probabilistic Models (TPMs) to exactly and efficiently compute the constrained posterior, and to leverage this signal to steer the denoising process of diffusion models. Specifically, this paper adopts a class of expressive TPMs termed Probabilistic Circuits (PCs). Building upon prior advances, we further scale up PCs and make them capable of guiding the image generation process of diffusion models. Empirical results suggest that our approach can consistently improve the overall quality and semantic coherence of inpainted images across three natural image datasets (i.e., CelebA-HQ, ImageNet, and LSUN) with only ~10% additional computational overhead brought by the TPM. Further, with the help of an image encoder and decoder, our method can readily accept semantic constraints on specific regions of the image, which opens up the potential for more controlled image generation tasks. In addition to proposing a new framework for constrained image generation, this paper highlights the benefit of more tractable models and motivates the development of expressive TPMs.

Reconstructing meshes from point clouds is an important task in fields such as robotics, autonomous systems, and medical imaging. This survey examines state-of-the-art learning-based approaches to mesh reconstruction, categorizing them into five paradigms: PointNet family, autoencoder architectures, deformation-based methods, point-move techniques, and primitive-based approaches. Each paradigm is explored in depth, detailing the primary approaches and their underlying methodologies. By comparing these techniques, our study serves as a comprehensive guide, and equips researchers and practitioners with the knowledge to navigate the landscape of learning-based mesh reconstruction techniques. The findings underscore the transformative potential of these methods, which often surpass traditional techniques in allowing detailed and efficient reconstructions.

There is an increasingly apparent need for validating the classifications made by deep learning systems in safety-critical applications like autonomous vehicle systems. A number of recent papers have proposed methods for detecting anomalous image data that appear different from known inlier data samples, including reconstruction-based autoencoders. Autoencoders optimize the compression of input data to a latent space of a dimensionality smaller than the original input and attempt to accurately reconstruct the input using that compressed representation. Since the latent vector is optimized to capture the salient features from the inlier class only, it is commonly assumed that images of objects from outside of the training class cannot effectively be compressed and reconstructed. Some thus consider reconstruction error as a kind of novelty measure. Here we suggest that reconstruction-based approaches fail to capture particular anomalies that lie far from known inlier samples in latent space but near the latent dimension manifold defined by the parameters of the model. We propose incorporating the Mahalanobis distance in latent space to better capture these out-of-distribution samples and our results show that this method often improves performance over the baseline approach.

We present a scalable 3D reconstruction model that addresses a critical limitation in offline feed-forward methods: their computational and memory requirements grow quadratically w.r.t. the number of input images. Our approach is built on the key insight that this bottleneck stems from the varying-length Key-Value (KV) space representation of scene geometry, which we distill into a fixed-size Multi-Layer Perceptron (MLP) via test-time training. VGG-T^3 (Visual Geometry Grounded Test Time Training) scales linearly w.r.t. the number of input views, similar to online models, and reconstructs a 1k image collection in just 54 seconds, achieving a 11.6times speed-up over baselines that rely on softmax attention. Since our method retains global scene aggregation capability, our point map reconstruction error outperforming other linear-time methods by large margins. Finally, we demonstrate visual localization capabilities of our model by querying the scene representation with unseen images.

Structural magnetic resonance imaging (MRI) images are sometimes corrupted over a contiguous set of slices, where acquisition, motion, hardware, or reconstruction effects leave a single slice or short interval inconsistent with its neighbors while the rest of the image remains usable. Such localized corruption can bias downstream morphometric analysis, yet discarding or reacquiring an otherwise usable image is costly. We formulate this as an image restoration problem: given the location of the affected interval, reconstruct those slices from the surrounding anatomical and imaging context. We propose SliceBridge, a framework for restoring corrupted slice intervals in T1-weighted MRI using rectified flow matching conditioned on the surrounding intact slices and their relative slice positions. Through-plane consistency is encouraged by coupling the slices within the interval through interval-correlated initial noise, a shared flow time, and synchronized sampling. The restored interval is then inserted back, leaving all other slices unchanged. We trained and validated the model on 9,877 T1-weighted brain MRI volumes from four datasets and evaluated it on 581 external subjects using clean interval withholding and controlled corruptions. Compared with a matched model that reconstructed target slices independently, SliceBridge reduced error in slice-to-slice changes within repaired intervals by 32.9%-41.3% across interval lengths and achieved higher SSIM at every interval length. In controlled-corruption cases, SliceBridge reduced the median error in regional brain volume estimates produced by a downstream segmentation model from 1.95% in corrupted volumes to 1.05%.

In many real-world scenarios, obtaining fully observed samples is prohibitively expensive or even infeasible, while partial and noisy observations are comparatively easy to collect. In this work, we study distribution restoration with abundant noisy samples, assuming the corruption process is available as a black-box generator. We show that this task can be framed as a one-sided entropic optimal transport problem and solved via an EM-like algorithm. We further provide a test criterion to determine whether the true underlying distribution is recoverable under per-sample information loss, and show that in otherwise unrecoverable cases, a small number of clean samples can render the distribution largely recoverable. Building on these insights, we introduce SFBD-OMNI, a bridge model-based framework that maps corrupted sample distributions to the ground-truth distribution. Our method generalizes Stochastic Forward-Backward Deconvolution (SFBD; Lu et al., 2025) to handle arbitrary measurement models beyond Gaussian corruption. Experiments across benchmark datasets and diverse measurement settings demonstrate significant improvements in both qualitative and quantitative performance.

Sparse-view X-ray 3D reconstruction is essential for reducing radiation exposure, but recovering a density field from a handful of X-ray projections is severely ill-posed. Recently, 3D Gaussian Splatting has achieved state-of-the-art performance in sparse-view reconstruction by representing the volume using explicit, optimized primitives, but it requires dozens of projected views. With fewer views, reconstruction quality degrades severely since the explicit primitives are optimized freely without any anatomical information. Anatomical structures, in contrast, share similar geometry and density across a population. Their variations are bounded within a limited range that statistical shape models can capture. This paper proposes a shape-guided Gaussian splatting framework for sparse-view X-ray 3D reconstructions. Our contribution lies in driving Gaussian positions toward anatomically valid configurations, alongside atlas-based density regularization. Our method ensures anatomically consistent reconstruction and improves PSNR by 2.83 dB over a state-of-the-art Gaussian splatting baseline with as few as 5 views. Code Available: https://github.com/polyshape-lab/ShapeGuidedGaussian

Despite recent progress, recovering parametric CAD construction sequences from geometric input, such as meshes or point clouds, is a key challenge for design and manufacturing, as existing CAD reconstruction and generation methods are largely restricted to difficult-to-edit formats like meshes or Breps or editable simple sketch-and-extrude pipelines and low-complexity datasets. We introduce CADFit, a hybrid optimization-based CAD reconstruction framework that recovers complex, editable CAD construction sequences from meshes by incrementally fitting and validating parametric operations using geometric feedback. Our approach is distinguished by formulating reconstruction as an IoU-driven optimization over structured CAD programs and supporting a rich set of operations, including extrusions, revolutions, fillets, and chamfers. Experiments on multiple CAD benchmarks show that CADFit outperforms state-of-the-art mesh-to-CAD methods in volumetric Intersection-over-Union and Chamfer Distance, while substantially reducing the Invalid Ratio of reconstructed CAD programs, particularly for complex designs. We further present a multimodal pipeline that enables end-to-end reconstruction of CAD construction sequences from images by combining image-based geometry reconstruction with CADFit. By enabling accurate reconstruction of higher-complexity CAD models, CADFit provides a practical foundation for generating richer datasets and advancing future learning-based approaches to CAD reverse engineering. The code is available at: https://github.com/ghadinehme/CADFit.

Inferring the 3D structure underlying a set of multi-view images typically requires solving two co-dependent tasks -- accurate 3D reconstruction requires precise camera poses, and predicting camera poses relies on (implicitly or explicitly) modeling the underlying 3D. The classical framework of analysis by synthesis casts this inference as a joint optimization seeking to explain the observed pixels, and recent instantiations learn expressive 3D representations (e.g., Neural Fields) with gradient-descent-based pose refinement of initial pose estimates. However, given a sparse set of observed views, the observations may not provide sufficient direct evidence to obtain complete and accurate 3D. Moreover, large errors in pose estimation may not be easily corrected and can further degrade the inferred 3D. To allow robust 3D reconstruction and pose estimation in this challenging setup, we propose SparseAGS, a method that adapts this analysis-by-synthesis approach by: a) including novel-view-synthesis-based generative priors in conjunction with photometric objectives to improve the quality of the inferred 3D, and b) explicitly reasoning about outliers and using a discrete search with a continuous optimization-based strategy to correct them. We validate our framework across real-world and synthetic datasets in combination with several off-the-shelf pose estimation systems as initialization. We find that it significantly improves the base systems' pose accuracy while yielding high-quality 3D reconstructions that outperform the results from current multi-view reconstruction baselines.

Although deep learning (DL) has received much attention in accelerated magnetic resonance imaging (MRI), recent studies show that tiny input perturbations may lead to instabilities of DL-based MRI reconstruction models. However, the approaches of robustifying these models are underdeveloped. Compared to image classification, it could be much more challenging to achieve a robust MRI image reconstruction network considering its regression-based learning objective, limited amount of training data, and lack of efficient robustness metrics. To circumvent the above limitations, our work revisits the problem of DL-based image reconstruction through the lens of robust machine learning. We find a new instability source of MRI image reconstruction, i.e., the lack of reconstruction robustness against spatial transformations of an input, e.g., rotation and cutout. Inspired by this new robustness metric, we develop a robustness-aware image reconstruction method that can defend against both pixel-wise adversarial perturbations as well as spatial transformations. Extensive experiments are also conducted to demonstrate the effectiveness of our proposed approaches.

Reconstructing articulated objects with multiple movable parts is essential for understanding object structure and enabling physical interaction. However, this reconstruction task poses significant challenges due to the entanglement of geometry, appearance, and motion parameters during optimization. Existing methods rely primarily on photometric supervision, which commonly fails to disentangle these interdependent components, resulting in poor part decomposition with blurred boundaries and geometric artifacts. To address this limitation, we introduce StructureGS, a reconstruction framework for articulated objects that integrates structure-aware guidance into 3D Gaussian Splatting. Our approach leverages oriented bounding boxes of object parts to enforce two key structural properties: spatial coherence, which constrains each part's geometry to remain compact and spatially coherent within its designated region, and structural connectivity, which enforces physically plausible contact relationships between adjacent parts. These properties are realized through structure-aware losses that inject explicit structural constraints into the optimization process. Extensive experiments demonstrate that our method achieves state-of-the-art performance in articulated object reconstruction, producing high-quality results with well-defined part geometries.

Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear inverse problems in noiseless settings, which significantly under-represents the complexity of real-world problems. In this work, we extend diffusion solvers to efficiently handle general noisy (non)linear inverse problems via approximation of the posterior sampling. Interestingly, the resulting posterior sampling scheme is a blended version of diffusion sampling with the manifold constrained gradient without a strict measurement consistency projection step, yielding a more desirable generative path in noisy settings compared to the previous studies. Our method demonstrates that diffusion models can incorporate various measurement noise statistics such as Gaussian and Poisson, and also efficiently handle noisy nonlinear inverse problems such as Fourier phase retrieval and non-uniform deblurring. Code available at https://github.com/DPS2022/diffusion-posterior-sampling

Multi-view 3D reconstruction has achieved remarkable progress with the advent of feed-forward 3D reconstruction models. However, these models are typically trained and evaluated under ideal, degradation-free imaging conditions, whereas real-world observations often contain degradations that differ significantly from such settings. Improving robustness for multi-view 3D reconstruction under degraded conditions therefore remains an important challenge. We present Geometry-Aware Representation Denoising (GARD), a novel framework that performs diffusion-based multi-view restoration directly in the feature space of a feed-forward 3D reconstruction model. This design exploits the geometry-aware feature representations of the 3D reconstructor to effectively recover accurate scene geometry. Furthermore, by employing an additional RGB image decoder, the refined representations can also be used to restore high-quality RGB images, thereby enabling the simultaneous recovery of 3D scene geometry and high-quality imagery. Comprehensive experiments on the Depth Anything 3 (DA3) benchmark demonstrate the effectiveness of the proposed GARD framework.

Model attribution is a critical component of deep neural networks (DNNs) for its interpretability to complex models. Recent studies bring up attention to the security of attribution methods as they are vulnerable to attribution attacks that generate similar images with dramatically different attributions. Existing works have been investigating empirically improving the robustness of DNNs against those attacks; however, none of them explicitly quantifies the actual deviations of attributions. In this work, for the first time, a constrained optimization problem is formulated to derive an upper bound that measures the largest dissimilarity of attributions after the samples are perturbed by any noises within a certain region while the classification results remain the same. Based on the formulation, different practical approaches are introduced to bound the attributions above using Euclidean distance and cosine similarity under both ell_2 and ell_infty-norm perturbations constraints. The bounds developed by our theoretical study are validated on various datasets and two different types of attacks (PGD attack and IFIA attribution attack). Over 10 million attacks in the experiments indicate that the proposed upper bounds effectively quantify the robustness of models based on the worst-case attribution dissimilarities.

Learning spatial-temporal correspondences in cardiac motion from images is important for understanding the underlying dynamics of cardiac anatomical structures. Many methods explicitly impose smoothness constraints such as the L_2 norm on the displacement vector field (DVF), while usually ignoring biomechanical feasibility in the transformation. Other geometric constraints either regularize specific regions of interest such as imposing incompressibility on the myocardium or introduce additional steps such as training a separate network-based regularizer on physically simulated datasets. In this work, we propose an explicit biomechanics-informed prior as regularization on the predicted DVF in modeling a more generic biomechanically plausible transformation within all cardiac structures without introducing additional training complexity. We validate our methods on two publicly available datasets in the context of 2D MRI data and perform extensive experiments to illustrate the effectiveness and robustness of our proposed methods compared to other competing regularization schemes. Our proposed methods better preserve biomechanical properties by visual assessment and show advantages in segmentation performance using quantitative evaluation metrics. The code is publicly available at https://github.com/Voldemort108X/bioinformed_reg.

We introduce GRM, a large-scale reconstructor capable of recovering a 3D asset from sparse-view images in around 0.1s. GRM is a feed-forward transformer-based model that efficiently incorporates multi-view information to translate the input pixels into pixel-aligned Gaussians, which are unprojected to create a set of densely distributed 3D Gaussians representing a scene. Together, our transformer architecture and the use of 3D Gaussians unlock a scalable and efficient reconstruction framework. Extensive experimental results demonstrate the superiority of our method over alternatives regarding both reconstruction quality and efficiency. We also showcase the potential of GRM in generative tasks, i.e., text-to-3D and image-to-3D, by integrating it with existing multi-view diffusion models. Our project website is at: https://justimyhxu.github.io/projects/grm/.

In various imaging problems, we only have access to compressed measurements of the underlying signals, hindering most learning-based strategies which usually require pairs of signals and associated measurements for training. Learning only from compressed measurements is impossible in general, as the compressed observations do not contain information outside the range of the forward sensing operator. We propose a new end-to-end self-supervised framework that overcomes this limitation by exploiting the equivariances present in natural signals. Our proposed learning strategy performs as well as fully supervised methods. Experiments demonstrate the potential of this framework on inverse problems including sparse-view X-ray computed tomography on real clinical data and image inpainting on natural images. Code has been made available at: https://github.com/edongdongchen/EI.

MRI reconstruction is an inherently ill-posed inverse problem, since incomplete measurements admit many plausible solutions. This ambiguity becomes more severe under high acceleration, where pixel-domain continuous predictors tend to average over feasible reconstructions and suppress high-frequency anatomy. We address this limitation by moving reconstruction to discrete multi-scale latent space and posing it as autoregressive next-acceleration-scale prediction. Leveraging discrete priors proven effective in visual autoregressive modeling, our method restricts the solution to compact sequences of codebook tokens, enabling sharp reconstructions even from extremely sparse measurements. This discrete autoregressive formulation also aligns naturally with modern large language model post-training techniques. Building on this observation, we introduce on-policy privileged information distillation for visual autoregressive modeling, where a teacher is provided training only privileged context that is unavailable at inference, in our case fully sampled acquisitions, and supervises a student trained on its own rollouts, leading to consistent reconstruction gains. Through extensive experiments on the fastMRI benchmark, we show that our approach delivers improved reconstruction performance across diverse sampling patterns under extreme undersampling. Project website is https://yilmazkorkmaz1.github.io/discrete-mri-reconstruction-opd/{here}.

The annealing phase is a pivotal convergence stage in LLM pre-training that ultimately determines final model quality. However, effectively selecting training data during this phase remains a key challenge. Current strategies rely on empirical heuristics, such as domain filtering or context extension, which lack a principled grounding in optimization theory. In this work, we characterize the annealing phase through the lens of the loss landscape's spectral geometry. We argue that optimal convergence requires gradient updates to satisfy heterogeneous constraints across different eigen-directions. Building on this insight, we formulate data selection as a problem of satisfying these directional constraints. To this end, we propose DiReCT (Directionally-Restrained Constrained Training), a novel framework that reformulates sample selection in the annealing stage as a constrained optimization problem. By imposing explicit directional constraints on per-sample gradients based on the spectral properties of the Hessian, DiReCT identifies samples that align with the optimal curvature-aware descent path. Extensive experiments across various model scales demonstrate that DiReCT consistently achieves state-of-the-art performance. For future research, code is available at https://github.com/xuyj233/Direct.

Post-training quantization is widely used for compressing large neural networks, but aggressive low-bit quantization can significantly degrade model quality. A common remedy is to augment the quantized weights with a low-rank correction, leading to approximations of the form Wapprox Q+LR. In this paper, we study this low-precision plus low-rank representation through the layer-wise reconstruction objective |XW-X(Q+LR)|_F^2, where X is a calibration matrix. We establish, to our knowledge, the first information-theoretic lower bounds for this problem under finite-alphabet and bounded low-rank compensation constraints. We then propose GPTQ-intrinsic LoRA, a training-free algorithm that incorporates the low-rank correction directly into a GPTQ-style quantization pass by appropriately augmenting the calibration Hessian. For the choice L=V_r, where V_r contains the top right singular vectors of X, we prove layer-wise reconstruction error bounds in which the usual GPTQ dependence on |X|_F^2 is replaced by the rank-r residual |X-X_r|_F^2, up to regularization terms. Under natural structural assumptions, these bounds match the information-theoretic lower bounds in their dominant scaling, up to constants and mild factors. We also introduce Bid-Up, a fixed-grid quantization refinement step that can be alternated with optimal low-rank compensation with guaranteed non-increasing layer-wise reconstruction error. Experiments on Qwen3 language models and DeiT vision transformers show that GPTQ-intrinsic LoRA improves over GPTQ and GPTQ followed by low-rank compensation, with additional gains from refinement loops.

We consider the problem of reconstructing a full 360{\deg} photographic model of an object from a single image of it. We do so by fitting a neural radiance field to the image, but find this problem to be severely ill-posed. We thus take an off-the-self conditional image generator based on diffusion and engineer a prompt that encourages it to "dream up" novel views of the object. Using an approach inspired by DreamFields and DreamFusion, we fuse the given input view, the conditional prior, and other regularizers in a final, consistent reconstruction. We demonstrate state-of-the-art reconstruction results on benchmark images when compared to prior methods for monocular 3D reconstruction of objects. Qualitatively, our reconstructions provide a faithful match of the input view and a plausible extrapolation of its appearance and 3D shape, including to the side of the object not visible in the image.

Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest shift/imbalance in covariates (i.e., secondary non-imaging data). Controlling for such nuisance variables is common within standard statistical analysis, but the ideas do not directly apply to overparameterized models. Consequently, recent work has shown how strategies from invariant representation learning provides a meaningful starting point, but the current repertoire of methods is limited to accounting for shifts/imbalances in just a couple of covariates at a time. In this paper, we show how viewing this problem from the perspective of Category theory provides a simple and effective solution that completely avoids elaborate multi-stage training pipelines that would otherwise be needed. We show the effectiveness of this approach via extensive experiments on real datasets. Further, we discuss how this style of formulation offers a unified perspective on at least 5+ distinct problem settings, from self-supervised learning to matching problems in 3D reconstruction.

Reconstruction-based methods are a dominant paradigm in time series anomaly detection (TSAD), however, their near-universal reliance on Mean Squared Error (MSE) loss results in statistically flawed reconstruction residuals. This fundamental weakness leads to noisy, unstable anomaly scores, hindering reliable detection. To address this, we propose Constrained Gaussian-Noise Optimization and Smoothing (COGNOS), a universal, model-agnostic enhancement framework that tackles this issue at its source. COGNOS introduces a novel Gaussian-White Noise Regularization strategy during training, which directly constrains the model's output residuals to conform to a Gaussian white noise distribution. This engineered statistical property creates the ideal precondition for our second contribution: Adaptive Residual Kalman Smoother that operates as a statistically robust estimator to denoise the raw anomaly scores. Extensive experiments on multiple benchmarks demonstrate that COGNOS consistently enhances the performance of state-of-the-art backbones significantly, validating the efficacy of coupling statistical regularization with adaptive filtering.

This paper focuses on the development of a space-variant regularization model for solving an under-determined linear inverse problem. The case study is a medical image reconstruction from few-view tomographic noisy data. The primary objective of the proposed optimization model is to achieve a good balance between denoising and the preservation of fine details and edges, overcoming the performance of the popular and largely used Total Variation (TV) regularization through the application of appropriate pixel-dependent weights. The proposed strategy leverages the role of gradient approximations for the computation of the space-variant TV weights. For this reason, a convolutional neural network is designed, to approximate both the ground truth image and its gradient using an elastic loss function in its training. Additionally, the paper provides a theoretical analysis of the proposed model, showing the uniqueness of its solution, and illustrates a Chambolle-Pock algorithm tailored to address the specific problem at hand. This comprehensive framework integrates innovative regularization techniques with advanced neural network capabilities, demonstrating promising results in achieving high-quality reconstructions from low-sampled tomographic data.

We present SHINOBI, an end-to-end framework for the reconstruction of shape, material, and illumination from object images captured with varying lighting, pose, and background. Inverse rendering of an object based on unconstrained image collections is a long-standing challenge in computer vision and graphics and requires a joint optimization over shape, radiance, and pose. We show that an implicit shape representation based on a multi-resolution hash encoding enables faster and robust shape reconstruction with joint camera alignment optimization that outperforms prior work. Further, to enable the editing of illumination and object reflectance (i.e. material) we jointly optimize BRDF and illumination together with the object's shape. Our method is class-agnostic and works on in-the-wild image collections of objects to produce relightable 3D assets for several use cases such as AR/VR, movies, games, etc. Project page: https://shinobi.aengelhardt.com Video: https://www.youtube.com/watch?v=iFENQ6AcYd8&feature=youtu.be

We revisit the problem of large-scale bundle adjustment and propose a technique called Multidirectional Conjugate Gradients that accelerates the solution of the normal equation by up to 61%. The key idea is that we enlarge the search space of classical preconditioned conjugate gradients to include multiple search directions. As a consequence, the resulting algorithm requires fewer iterations, leading to a significant speedup of large-scale reconstruction, in particular for denser problems where traditional approaches notoriously struggle. We provide a number of experimental ablation studies revealing the robustness to variations in the hyper-parameters and the speedup as a function of problem density.

In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to obtain lower dimensional bundles. Local approximations obtained by local PCAs are collected into a rank k tangent subbundle on R^d, k<d, which we call a principal subbundle. This determines a sub-Riemannian metric on R^d. We show that sub-Riemannian geodesics with respect to this metric can successfully be applied to a number of important problems, such as: explicit construction of an approximating submanifold M, construction of a representation of the point-cloud in R^k, and computation of distances between observations, taking the learned geometry into account. The reconstruction is guaranteed to equal the true submanifold in the limit case where tangent spaces are estimated exactly. Via simulations, we show that the framework is robust when applied to noisy data. Furthermore, the framework generalizes to observations on an a priori known Riemannian manifold.

Reconstruction and joint embedding have emerged as two leading paradigms in Self Supervised Learning (SSL). Reconstruction methods focus on recovering the original sample from a different view in input space. On the other hand, joint embedding methods align the representations of different views in latent space. Both approaches offer compelling advantages, yet practitioners lack clear guidelines for choosing between them. In this work, we unveil the core mechanisms that distinguish each paradigm. By leveraging closed form solutions for both approaches, we precisely characterize how the view generation process, e.g. data augmentation, impacts the learned representations. We then demonstrate that, unlike supervised learning, both SSL paradigms require a minimal alignment between augmentations and irrelevant features to achieve asymptotic optimality with increasing sample size. Our findings indicate that in scenarios where these irrelevant features have a large magnitude, joint embedding methods are preferable because they impose a strictly weaker alignment condition compared to reconstruction based methods. These results not only clarify the trade offs between the two paradigms but also substantiate the empirical success of joint embedding approaches on real world challenging datasets.

Existing polygonal surface reconstruction methods heavily depend on input completeness and struggle with incomplete point clouds. We argue that while current point cloud completion techniques may recover missing points, they are not optimized for polygonal surface reconstruction, where the parametric representation of underlying surfaces remains overlooked. To address this gap, we introduce parametric completion, a novel paradigm for point cloud completion, which recovers parametric primitives instead of individual points to convey high-level geometric structures. Our presented approach, PaCo, enables high-quality polygonal surface reconstruction by leveraging plane proxies that encapsulate both plane parameters and inlier points, proving particularly effective in challenging scenarios with highly incomplete data. Comprehensive evaluations of our approach on the ABC dataset establish its effectiveness with superior performance and set a new standard for polygonal surface reconstruction from incomplete data. Project page: https://parametric-completion.github.io.

Recent monocular 3D shape reconstruction methods have shown promising zero-shot results on object-segmented images without any occlusions. However, their effectiveness is significantly compromised in real-world conditions, due to imperfect object segmentation by off-the-shelf models and the prevalence of occlusions. To effectively address these issues, we propose a unified regression model that integrates segmentation and reconstruction, specifically designed for occlusion-aware 3D shape reconstruction. To facilitate its reconstruction in the wild, we also introduce a scalable data synthesis pipeline that simulates a wide range of variations in objects, occluders, and backgrounds. Training on our synthetic data enables the proposed model to achieve state-of-the-art zero-shot results on real-world images, using significantly fewer parameters than competing approaches.

Reconstructing 3D representations from 2D inputs is a fundamental task in computer vision and graphics, serving as a cornerstone for understanding and interacting with the physical world. While traditional methods achieve high fidelity, they are limited by slow per-scene optimization or category-specific training, which hinders their practical deployment and scalability. Hence, generalizable feed-forward 3D reconstruction has witnessed rapid development in recent years. By learning a model that maps images directly to 3D representations in a single forward pass, these methods enable efficient reconstruction and robust cross-scene generalization. Our survey is motivated by a critical observation: despite the diverse geometric output representations, ranging from implicit fields to explicit primitives, existing feed-forward approaches share similar high-level architectural patterns, such as image feature extraction backbones, multi-view information fusion mechanisms, and geometry-aware design principles. Consequently, we abstract away from these representation differences and instead focus on model design, proposing a novel taxonomy centered on model design strategies that are agnostic to the output format. Our proposed taxonomy organizes the research directions into five key problems that drive recent research development: feature enhancement, geometry awareness, model efficiency, augmentation strategies and temporal-aware models. To support this taxonomy with empirical grounding and standardized evaluation, we further comprehensively review related benchmarks and datasets, and extensively discuss and categorize real-world applications based on feed-forward 3D models. Finally, we outline future directions to address open challenges such as scalability, evaluation standards, and world modeling.

While 3D body reconstruction methods have made remarkable progress recently, it remains difficult to acquire the sufficiently accurate and numerous 3D supervisions required for training. In this paper, we propose KNOWN, a framework that effectively utilizes body KNOWledge and uNcertainty modeling to compensate for insufficient 3D supervisions. KNOWN exploits a comprehensive set of generic body constraints derived from well-established body knowledge. These generic constraints precisely and explicitly characterize the reconstruction plausibility and enable 3D reconstruction models to be trained without any 3D data. Moreover, existing methods typically use images from multiple datasets during training, which can result in data noise (e.g., inconsistent joint annotation) and data imbalance (e.g., minority images representing unusual poses or captured from challenging camera views). KNOWN solves these problems through a novel probabilistic framework that models both aleatoric and epistemic uncertainty. Aleatoric uncertainty is encoded in a robust Negative Log-Likelihood (NLL) training loss, while epistemic uncertainty is used to guide model refinement. Experiments demonstrate that KNOWN's body reconstruction outperforms prior weakly-supervised approaches, particularly on the challenging minority images.

Magnetic resonance elastography (MRE) is a noninvasive imaging modality for quantifying the viscoelastic properties of soft tissues from shear wave propagation. Recovering the complex-valued shear modulus from measured displacement fields leads to a severely ill-posed inverse problem, particularly in the presence of noise and limited boundary excitations. We investigate adjoint-based optimization, convolutional neural network (CNN) reconstruction, and a hybrid framework combining both approaches. The forward model is based on a scalar form of the modified stationary Stokes system with a complex shear modulus. We establish well-posedness of the forward problem, existence of minimizers, and first-order optimality conditions for the adjoint-based formulation, and implement a nonlinear conjugate-gradient method with Armijo line search. While PDE-constrained optimization can accurately refine coefficient reconstructions, its performance depends strongly on initialization. We therefore construct a two-dimensional CNN that maps complex-valued displacement measurements to spatially varying complex shear modulus fields and provides rapid, informative initial reconstructions. The proposed hybrid method uses the CNN reconstruction to initialize the adjoint-based optimization, yielding faster convergence and improved accuracy. The CNN is trained on coefficient fields containing individual perturbations and tested on both individual and previously unseen combined configurations. Numerical experiments demonstrate that the CNN generalizes to these more challenging configurations, while subsequent PDE-constrained optimization further refines the reconstructed coefficient. These results demonstrate the potential of combining data-driven initialization with physics-based optimization for efficient and accurate MRE reconstruction.

Generative Adversarial Networks (GANs) struggle to generate structured objects like molecules and game maps. The issue is that structured objects must satisfy hard requirements (e.g., molecules must be chemically valid) that are difficult to acquire from examples alone. As a remedy, we propose Constrained Adversarial Networks (CANs), an extension of GANs in which the constraints are embedded into the model during training. This is achieved by penalizing the generator proportionally to the mass it allocates to invalid structures. In contrast to other generative models, CANs support efficient inference of valid structures (with high probability) and allows to turn on and off the learned constraints at inference time. CANs handle arbitrary logical constraints and leverage knowledge compilation techniques to efficiently evaluate the disagreement between the model and the constraints. Our setup is further extended to hybrid logical-neural constraints for capturing very complex constraints, like graph reachability. An extensive empirical analysis shows that CANs efficiently generate valid structures that are both high-quality and novel.

In image editing employing diffusion models, it is crucial to preserve the reconstruction quality of the original image while changing its style. Although existing methods ensure reconstruction quality through optimization, a drawback of these is the significant amount of time required for optimization. In this paper, we propose negative-prompt inversion, a method capable of achieving equivalent reconstruction solely through forward propagation without optimization, thereby enabling much faster editing processes. We experimentally demonstrate that the reconstruction quality of our method is comparable to that of existing methods, allowing for inversion at a resolution of 512 pixels and with 50 sampling steps within approximately 5 seconds, which is more than 30 times faster than null-text inversion. Reduction of the computation time by the proposed method further allows us to use a larger number of sampling steps in diffusion models to improve the reconstruction quality with a moderate increase in computation time.

Stable diffusion models represent the state-of-the-art in data synthesis across diverse domains and hold transformative potential for applications in science and engineering, e.g., by facilitating the discovery of novel solutions and simulating systems that are computationally intractable to model explicitly. While there is increasing effort to incorporate physics-based constraints into generative models, existing techniques are either limited in their applicability to latent diffusion frameworks or lack the capability to strictly enforce domain-specific constraints. To address this limitation this paper proposes a novel integration of stable diffusion models with constrained optimization frameworks, enabling the generation of outputs satisfying stringent physical and functional requirements. The effectiveness of this approach is demonstrated through material design experiments requiring adherence to precise morphometric properties, challenging inverse design tasks involving the generation of materials inducing specific stress-strain responses, and copyright-constrained content generation tasks. All code has been released at https://github.com/RAISELab-atUVA/Constrained-Stable-Diffusion.

This paper tackles the challenge of robust reconstruction, i.e., the task of reconstructing a 3D scene from a set of inconsistent multi-view images. Some recent works have attempted to simultaneously remove image inconsistencies and perform reconstruction by integrating image degradation modeling into neural 3D scene representations. However, these methods rely heavily on dense observations for robustly optimizing model parameters. To address this issue, we propose to decouple robust reconstruction into two subtasks: restoration and reconstruction, which naturally simplifies the optimization process. To this end, we introduce UniVerse, a unified framework for robust reconstruction based on a video diffusion model. Specifically, UniVerse first converts inconsistent images into initial videos, then uses a specially designed video diffusion model to restore them into consistent images, and finally reconstructs the 3D scenes from these restored images. Compared with case-by-case per-view degradation modeling, the diffusion model learns a general scene prior from large-scale data, making it applicable to diverse image inconsistencies. Extensive experiments on both synthetic and real-world datasets demonstrate the strong generalization capability and superior performance of our method in robust reconstruction. Moreover, UniVerse can control the style of the reconstructed 3D scene. Project page: https://jin-cao-tma.github.io/UniVerse.github.io/

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

Modern reconstruction techniques can effectively model complex 3D scenes from sparse 2D views. However, automatically assessing the quality of novel views and identifying artifacts is challenging due to the lack of ground truth images and the limitations of no-reference image metrics in predicting detailed artifact maps. The absence of such quality metrics hinders accurate predictions of the quality of generated views and limits the adoption of post-processing techniques, such as inpainting, to enhance reconstruction quality. In this work, we propose a new no-reference metric, Puzzle Similarity, which is designed to localize artifacts in novel views. Our approach utilizes image patch statistics from the input views to establish a scene-specific distribution that is later used to identify poorly reconstructed regions in the novel views. We test and evaluate our method in the context of 3D reconstruction; to this end, we collected a novel dataset of human quality assessment in unseen reconstructed views. Through this dataset, we demonstrate that our method can not only successfully localize artifacts in novel views, correlating with human assessment, but do so without direct references. Surprisingly, our metric outperforms both no-reference metrics and popular full-reference image metrics. We can leverage our new metric to enhance applications like automatic image restoration, guided acquisition, or 3D reconstruction from sparse inputs.

We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically involves an underlying projection process that maps the original hypergraph onto a graph, and is common in graph-based analysis. While hypergraph projection can potentially lead to loss of higher-order relations, there exists very limited studies on the consequences of doing so, as well as its remediation. This work fills this gap by doing two things: (1) we develop analysis based on graph and set theory, showing two ubiquitous patterns of hyperedges that are root to structural information loss in all hypergraph projections; we also quantify the combinatorial impossibility of recovering the lost higher-order structures if no extra help is provided; (2) we still seek to recover the lost higher-order structures in hypergraph projection, and in light of (1)'s findings we propose to relax the problem into a learning-based setting. Under this setting, we develop a learning-based hypergraph reconstruction method based on an important statistic of hyperedge distributions that we find. Our reconstruction method is evaluated on 8 real-world datasets under different settings, and exhibits consistently good performance. We also demonstrate benefits of the reconstructed hypergraphs via use cases of protein rankings and link predictions.

Generative 3D reconstruction shows strong potential in incomplete observations. While sparse-view and single-image reconstruction are well-researched, partial observation remains underexplored. In this context, dense views are accessible only from a specific angular range, with other perspectives remaining inaccessible. This task presents two main challenges: (i) limited View Range: observations confined to a narrow angular scope prevent effective traditional interpolation techniques that require evenly distributed perspectives. (ii) inconsistent Generation: views created for invisible regions often lack coherence with both visible regions and each other, compromising reconstruction consistency. To address these challenges, we propose \method, a novel training-free approach that integrates the local dense observations and multi-source priors for reconstruction. Our method introduces a fusion-based strategy to effectively align these priors in DDIM sampling, thereby generating multi-view consistent images to supervise invisible views. We further design an iterative refinement strategy, which uses the geometric structures of the object to enhance reconstruction quality. Extensive experiments on multiple datasets show the superiority of our method over SOTAs, especially in invisible regions.

Generating complete 3D assets from sparse, unposed images requires preserving observed geometry while completing unseen regions. Joint reconstruction and generation offers a way to address both goals: reconstruction recovers the geometry observed in the input images, while generation contributes learned shape priors. However, combining camera-relative reconstruction with canonical-space generation introduces a coordinate mismatch that makes direct geometric interaction more difficult. Moreover, conditioning each 3D location on all views without accounting for their relevance may mix useful geometric evidence with unrelated image content, hindering local detail recovery. We present UniForge3D, which jointly models reconstruction and generation in a shared anchor-guided space, resolving their coordinate mismatch. This space follows the anchor view's azimuth while keeping the object upright. The two branches exchange features bidirectionally to predict per-view point maps and a complete sparse voxel structure. We further condition point-map prediction on the generated structure to establish pixel-to-voxel correspondences and select the most informative input view for each voxel. Features from the selected views then guide detailed shape generation, helping preserve observed geometric details. Our method achieves state-of-the-art appearance and geometry results on Toys4K and GSO, generating complete 3D assets with improved fidelity. Project webpage: https://xishuxishu.github.io/uniforge3d-project/

Sparse-view 3D reconstruction is essential for modeling scenes from casual captures, but remain challenging for non-generative reconstruction. Existing diffusion-based approaches mitigates this issues by synthesizing novel views, but they often condition on only one or two capture frames, which restricts geometric consistency and limits scalability to large or diverse scenes. We propose AnyRecon, a scalable framework for reconstruction from arbitrary and unordered sparse inputs that preserves explicit geometric control while supporting flexible conditioning cardinality. To support long-range conditioning, our method constructs a persistent global scene memory via a prepended capture view cache, and removes temporal compression to maintain frame-level correspondence under large viewpoint changes. Beyond better generative model, we also find that the interplay between generation and reconstruction is crucial for large-scale 3D scenes. Thus, we introduce a geometry-aware conditioning strategy that couples generation and reconstruction through an explicit 3D geometric memory and geometry-driven capture-view retrieval. To ensure efficiency, we combine 4-step diffusion distillation with context-window sparse attention to reduce quadratic complexity. Extensive experiments demonstrate robust and scalable reconstruction across irregular inputs, large viewpoint gaps, and long trajectories.

Estimating the pose of an object from a monocular image is an inverse problem fundamental in computer vision. The ill-posed nature of this problem requires incorporating deformation priors to solve it. In practice, many materials do not perceptibly shrink or extend when manipulated, constituting a powerful and well-known prior. Mathematically, this translates to the preservation of the Riemannian metric. Neural networks offer the perfect playground to solve the surface reconstruction problem as they can approximate surfaces with arbitrary precision and allow the computation of differential geometry quantities. This paper presents an approach to inferring continuous deformable surfaces from a sequence of images, which is benchmarked against several techniques and obtains state-of-the-art performance without the need for offline training.

Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers, acting as the prior of the distribution, while the information of the forward model can be granted at the sampling stage. Nonetheless, as the generative process remains in the same high dimensional (i.e. identical to data dimension) space, the models have not been extended to 3D inverse problems due to the extremely high memory and computational cost. In this paper, we combine the ideas from the conventional model-based iterative reconstruction with the modern diffusion models, which leads to a highly effective method for solving 3D medical image reconstruction tasks such as sparse-view tomography, limited angle tomography, compressed sensing MRI from pre-trained 2D diffusion models. In essence, we propose to augment the 2D diffusion prior with a model-based prior in the remaining direction at test time, such that one can achieve coherent reconstructions across all dimensions. Our method can be run in a single commodity GPU, and establishes the new state-of-the-art, showing that the proposed method can perform reconstructions of high fidelity and accuracy even in the most extreme cases (e.g. 2-view 3D tomography). We further reveal that the generalization capacity of the proposed method is surprisingly high, and can be used to reconstruct volumes that are entirely different from the training dataset.

3D reconstruction of dynamic scenes is a long-standing problem in computer graphics and increasingly difficult the less information is available. Shape-from-Template (SfT) methods aim to reconstruct a template-based geometry from RGB images or video sequences, often leveraging just a single monocular camera without depth information, such as regular smartphone recordings. Unfortunately, existing reconstruction methods are either unphysical and noisy or slow in optimization. To solve this problem, we propose a novel SfT reconstruction algorithm for cloth using a pre-trained neural surrogate model that is fast to evaluate, stable, and produces smooth reconstructions due to a regularizing physics simulation. Differentiable rendering of the simulated mesh enables pixel-wise comparisons between the reconstruction and a target video sequence that can be used for a gradient-based optimization procedure to extract not only shape information but also physical parameters such as stretching, shearing, or bending stiffness of the cloth. This allows to retain a precise, stable, and smooth reconstructed geometry while reducing the runtime by a factor of 400-500 compared to phi-SfT, a state-of-the-art physics-based SfT approach.

Recent developments in differentiable and neural rendering have made impressive breakthroughs in a variety of 2D and 3D tasks, e.g. novel view synthesis, 3D reconstruction. Typically, differentiable rendering relies on a dense viewpoint coverage of the scene, such that the geometry can be disambiguated from appearance observations alone. Several challenges arise when only a few input views are available, often referred to as sparse or few-shot neural rendering. As this is an underconstrained problem, most existing approaches introduce the use of regularisation, together with a diversity of learnt and hand-crafted priors. A recurring problem in sparse rendering literature is the lack of an homogeneous, up-to-date, dataset and evaluation protocol. While high-resolution datasets are standard in dense reconstruction literature, sparse rendering methods often evaluate with low-resolution images. Additionally, data splits are inconsistent across different manuscripts, and testing ground-truth images are often publicly available, which may lead to over-fitting. In this work, we propose the Sparse Rendering (SpaRe) dataset and benchmark. We introduce a new dataset that follows the setup of the DTU MVS dataset. The dataset is composed of 97 new scenes based on synthetic, high-quality assets. Each scene has up to 64 camera views and 7 lighting configurations, rendered at 1600x1200 resolution. We release a training split of 82 scenes to foster generalizable approaches, and provide an online evaluation platform for the validation and test sets, whose ground-truth images remain hidden. We propose two different sparse configurations (3 and 9 input images respectively). This provides a powerful and convenient tool for reproducible evaluation, and enable researchers easy access to a public leaderboard with the state-of-the-art performance scores. Available at: https://sparebenchmark.github.io/

Reconstructing object deformation from a single image remains a significant challenge in computer vision and graphics. Existing methods typically rely on multi-view video to recover deformation, limiting their applicability under constrained scenarios. To address this, we propose DeformSplat, a novel framework that effectively guides 3D Gaussian deformation from only a single image. Our method introduces two main technical contributions. First, we present Gaussian-to-Pixel Matching which bridges the domain gap between 3D Gaussian representations and 2D pixel observations. This enables robust deformation guidance from sparse visual cues. Second, we propose Rigid Part Segmentation consisting of initialization and refinement. This segmentation explicitly identifies rigid regions, crucial for maintaining geometric coherence during deformation. By combining these two techniques, our approach can reconstruct consistent deformations from a single image. Extensive experiments demonstrate that our approach significantly outperforms existing methods and naturally extends to various applications,such as frame interpolation and interactive object manipulation.

We propose a novel mixed-integer programming (MIP) formulation for generating precise sparse correspondences for highly non-rigid shapes. To this end, we introduce a projected Laplace-Beltrami operator (PLBO) which combines intrinsic and extrinsic geometric information to measure the deformation quality induced by predicted correspondences. We integrate the PLBO, together with an orientation-aware regulariser, into a novel MIP formulation that can be solved to global optimality for many practical problems. In contrast to previous methods, our approach is provably invariant to rigid transformations and global scaling, initialisation-free, has optimality guarantees, and scales to high resolution meshes with (empirically observed) linear time. We show state-of-the-art results for sparse non-rigid matching on several challenging 3D datasets, including data with inconsistent meshing, as well as applications in mesh-to-point-cloud matching.

We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in optimal-approximation theory, we train a network to decompose an implicit approximation operator by minimizing the reconstruction error in the learned basis over a chosen distribution of probe functions. For suitable distributions, they can be seen as an approximation of the Laplacian operator and its eigendecomposition, which are fundamental in geometry processing. Furthermore, our method recovers in a unified manner not only the spectral basis, but also the implicit metric's sampling density and the eigenvalues of the underlying operator. Notably, our unsupervised method makes no assumption on the data manifold, such as meshing or manifold dimensionality, allowing it to scale to arbitrary datasets of any dimension. On point clouds lying on surfaces in 3D and high-dimensional image manifolds, our approach yields meaningful spectral bases, that can resemble those of the Laplacian, without explicit construction of an operator. By replacing the traditional operator selection, construction, and eigendecomposition with a learning-based approach, our framework offers a principled, data-driven alternative to conventional pipelines. This opens new possibilities in geometry processing for unstructured data, particularly in high-dimensional spaces.

We present Wid3R, a feed-forward neural network for visual geometry reconstruction that supports wide field-of-view camera models. Prior methods typically assume that input images are rectified or captured with pinhole cameras, since both their architectures and training datasets are tailored to perspective images only. These assumptions limit their applicability in real-world scenarios that use fisheye or panoramic cameras and often require careful calibration and undistortion. In contrast, Wid3R is a generalizable multi-view 3D estimation method that can model wide field-of-view camera types. Our approach leverages a ray representation with spherical harmonics and a novel camera model token within the network, enabling distortion-aware 3D reconstruction. Furthermore, Wid3R is the first multi-view foundation model to support feed-forward 3D reconstruction directly from 360 imagery. It demonstrates strong zero-shot robustness and consistently outperforms prior methods, achieving improvements of up to +77.33 on Stanford2D3D.

Vector-quantized networks (VQNs) have exhibited remarkable performance across various tasks, yet they are prone to training instability, which complicates the training process due to the necessity for techniques such as subtle initialization and model distillation. In this study, we identify the local minima issue as the primary cause of this instability. To address this, we integrate an optimal transport method in place of the nearest neighbor search to achieve a more globally informed assignment. We introduce OptVQ, a novel vector quantization method that employs the Sinkhorn algorithm to optimize the optimal transport problem, thereby enhancing the stability and efficiency of the training process. To mitigate the influence of diverse data distributions on the Sinkhorn algorithm, we implement a straightforward yet effective normalization strategy. Our comprehensive experiments on image reconstruction tasks demonstrate that OptVQ achieves 100% codebook utilization and surpasses current state-of-the-art VQNs in reconstruction quality.

Diffusion models have recently emerged as powerful priors for solving inverse problems. While computed tomography (CT) is theoretically a linear inverse problem, it poses many practical challenges. These include correlated noise, artifact structures, reliance on system geometry, and misaligned value ranges, which make the direct application of diffusion models more difficult than in domains like natural image generation. To systematically evaluate how diffusion models perform in this context and compare them with established reconstruction methods, we introduce DM4CT, a comprehensive benchmark for CT reconstruction. DM4CT includes datasets from both medical and industrial domains with sparse-view and noisy configurations. To explore the challenges of deploying diffusion models in practice, we additionally acquire a high-resolution CT dataset at a high-energy synchrotron facility and evaluate all methods under real experimental conditions. We benchmark ten recent diffusion-based methods alongside seven strong baselines, including model-based, unsupervised, and supervised approaches. Our analysis provides detailed insights into the behavior, strengths, and limitations of diffusion models for CT reconstruction. The real-world dataset is publicly available at zenodo.org/records/15420527, and the codebase is open-sourced at github.com/DM4CT/DM4CT.

In this paper, we introduce a method for reconstructing 3D humans from a single image using a biomechanically accurate skeleton model. To achieve this, we train a transformer that takes an image as input and estimates the parameters of the model. Due to the lack of training data for this task, we build a pipeline to produce pseudo ground truth model parameters for single images and implement a training procedure that iteratively refines these pseudo labels. Compared to state-of-the-art methods for 3D human mesh recovery, our model achieves competitive performance on standard benchmarks, while it significantly outperforms them in settings with extreme 3D poses and viewpoints. Additionally, we show that previous reconstruction methods frequently violate joint angle limits, leading to unnatural rotations. In contrast, our approach leverages the biomechanically plausible degrees of freedom making more realistic joint rotation estimates. We validate our approach across multiple human pose estimation benchmarks. We make the code, models and data available at: https://isshikihugh.github.io/HSMR/

Recent advances in data-driven geometric multi-view 3D reconstruction foundation models (e.g., DUSt3R) have shown remarkable performance across various 3D vision tasks, facilitated by the release of large-scale, high-quality 3D datasets. However, as we observed, constrained by their matching-based principles, the reconstruction quality of existing models suffers significant degradation in challenging regions with limited matching cues, particularly in weakly textured areas and low-light conditions. To mitigate these limitations, we propose to harness the inherent robustness of monocular geometry estimation to compensate for the inherent shortcomings of matching-based methods. Specifically, we introduce a monocular-guided refinement module that integrates monocular geometric priors into multi-view reconstruction frameworks. This integration substantially enhances the robustness of multi-view reconstruction systems, leading to high-quality feed-forward reconstructions. Comprehensive experiments across multiple benchmarks demonstrate that our method achieves substantial improvements in both mutli-view camera pose estimation and point cloud accuracy.

We consider the problem of real-time reconstruction of urban air pollution maps. The task is challenging due to the heterogeneous sources of available data, the scarcity of direct measurements, the presence of noise, and the large surfaces that need to be considered. In this work, we introduce different reconstruction methods based on posing the problem on city graphs. Our strategies can be classified as fully data-driven, physics-driven, or hybrid, and we combine them with super-learning models. The performance of the methods is tested in the case of the inner city of Paris, France.

Reconstructing physics-based 3D assets -- geometry, materials, and illumination -- from multi-view images is a core problem in computer graphics and vision, and a prerequisite for realistic relighting and editing. Physics-based inverse rendering offers an accurate image-formation model, but is severely underconstrained: without strong priors, illumination is baked into materials, and reconstructions generalize poorly to novel views and lighting. Data-driven diffusion models, in contrast, predict visually plausible materials, yet their predictions rarely satisfy the rendering equation and are not directly usable for physics-based rendering. We bridge these two paradigms rather than replacing either. Our key idea is to treat the predictions of a state-of-the-art diffusion model not as target material values but as a similarity kernel for optimization: we introduce a regularization loss that penalizes deviations in the optimized material over surface regions where the diffusion predictions are near-constant, while leaving the optimization free to match the input images. Built on this regularizer, our end-to-end pipeline jointly reconstructs geometry, materials, and illumination, yielding high-quality assets that drop into standard rendering pipelines and relight faithfully. On the Synthetic4Relight, Stanford-ORB, and DTC-Synthetic datasets, our method significantly outperforms state-of-the-art baselines in both reconstruction accuracy and relighting quality.

Generalizable neural surface reconstruction techniques have attracted great attention in recent years. However, they encounter limitations of low confidence depth distribution and inaccurate surface reasoning due to the oversimplified volume rendering process employed. In this paper, we present Reconstruction TRansformer (ReTR), a novel framework that leverages the transformer architecture to redesign the rendering process, enabling complex render interaction modeling. It introduces a learnable meta-ray token and utilizes the cross-attention mechanism to simulate the interaction of rendering process with sampled points and render the observed color. Meanwhile, by operating within a high-dimensional feature space rather than the color space, ReTR mitigates sensitivity to projected colors in source views. Such improvements result in accurate surface assessment with high confidence. We demonstrate the effectiveness of our approach on various datasets, showcasing how our method outperforms the current state-of-the-art approaches in terms of reconstruction quality and generalization ability. Our code is available at https://github.com/YixunLiang/ReTR.

The demand for high-quality medical imaging in clinical practice and assisted diagnosis has made 3D image reconstruction in radiological imaging a key research focus. Artificial intelligence (AI) has emerged as a promising approach for improving reconstruction accuracy while reducing acquisition and processing time, thereby minimizing patient radiation exposure and discomfort and ultimately benefiting clinical diagnosis. This review surveys state-of-the-art AI-based 3D reconstruction algorithms in radiological imaging and organizes them into four representation families according to how the reconstructed target is parameterized: discrete grid representations, explicit basis expansion representations, explicit primitive representations, and implicit neural representations. In particular, the review clarifies the relationships among these representation forms and highlights radiance field methods as a specialized subtype of implicit neural representation. In addition, we summarize commonly used evaluation metrics and benchmark datasets for radiological image reconstruction. Finally, we discuss the current state of development, major challenges, and future research directions in this rapidly evolving field. Our project is available at: https://github.com/Bean-Young/AI4Radiology.

Diffusion bridge models establish probabilistic paths between arbitrary paired distributions and exhibit great potential for universal image restoration. Most existing methods merely treat them as simple variants of stochastic interpolants, lacking a unified analytical perspective. Besides, they indiscriminately reconstruct images through global noise injection and removal, inevitably distorting undegraded regions due to imperfect reconstruction. To address these challenges, we propose the Residual Diffusion Bridge Model (RDBM). Specifically, we theoretically reformulate the stochastic differential equations of generalized diffusion bridge and derive the analytical formulas of its forward and reverse processes. Crucially, we leverage the residuals from given distributions to modulate the noise injection and removal, enabling adaptive restoration of degraded regions while preserving intact others. Moreover, we unravel the fundamental mathematical essence of existing bridge models, all of which are special cases of RDBM and empirically demonstrate the optimality of our proposed models. Extensive experiments are conducted to demonstrate the state-of-the-art performance of our method both qualitatively and quantitatively across diverse image restoration tasks. Code is publicly available at https://github.com/MiliLab/RDBM.

We propose MeshLRM, a novel LRM-based approach that can reconstruct a high-quality mesh from merely four input images in less than one second. Different from previous large reconstruction models (LRMs) that focus on NeRF-based reconstruction, MeshLRM incorporates differentiable mesh extraction and rendering within the LRM framework. This allows for end-to-end mesh reconstruction by fine-tuning a pre-trained NeRF LRM with mesh rendering. Moreover, we improve the LRM architecture by simplifying several complex designs in previous LRMs. MeshLRM's NeRF initialization is sequentially trained with low- and high-resolution images; this new LRM training strategy enables significantly faster convergence and thereby leads to better quality with less compute. Our approach achieves state-of-the-art mesh reconstruction from sparse-view inputs and also allows for many downstream applications, including text-to-3D and single-image-to-3D generation. Project page: https://sarahweiii.github.io/meshlrm/

City-scale 3D reconstruction from satellite imagery presents the challenge of extreme viewpoint extrapolation, where our goal is to synthesize ground-level novel views from sparse orbital images with minimal parallax. This requires inferring nearly 90^circ viewpoint gaps from image sources with severely foreshortened facades and flawed textures, causing state-of-the-art reconstruction engines such as NeRF and 3DGS to fail. To address this problem, we propose two design choices tailored for city structures and satellite inputs. First, we model city geometry as a 2.5D height map, implemented as a Z-monotonic signed distance field (SDF) that matches urban building layouts from top-down viewpoints. This stabilizes geometry optimization under sparse, off-nadir satellite views and yields a watertight mesh with crisp roofs and clean, vertically extruded facades. Second, we paint the mesh appearance from satellite images via differentiable rendering techniques. While the satellite inputs may contain long-range, blurry captures, we further train a generative texture restoration network to enhance the appearance, recovering high-frequency, plausible texture details from degraded inputs. Our method's scalability and robustness are demonstrated through extensive experiments on large-scale urban reconstruction. For example, in our teaser figure, we reconstruct a 4,km^2 real-world region from only a few satellite images, achieving state-of-the-art performance in synthesizing photorealistic ground views. The resulting models are not only visually compelling but also serve as high-fidelity, application-ready assets for downstream tasks like urban planning and simulation. Project page can be found at https://pku-vcl-geometry.github.io/Orbit2Ground/.

The field of image generation is currently bifurcated into autoregressive (AR) models operating on discrete tokens and diffusion models utilizing continuous latents. This divide, rooted in the distinction between VQ-VAEs and VAEs, hinders unified modeling and fair benchmarking. Finite Scalar Quantization (FSQ) offers a theoretical bridge, yet vanilla FSQ suffers from a critical flaw: its equal-interval quantization can cause activation collapse. This mismatch forces a trade-off between reconstruction fidelity and information efficiency. In this work, we resolve this dilemma by simply replacing the activation function in original FSQ with a distribution-matching mapping to enforce a uniform prior. Termed iFSQ, this simple strategy requires just one line of code yet mathematically guarantees both optimal bin utilization and reconstruction precision. Leveraging iFSQ as a controlled benchmark, we uncover two key insights: (1) The optimal equilibrium between discrete and continuous representations lies at approximately 4 bits per dimension. (2) Under identical reconstruction constraints, AR models exhibit rapid initial convergence, whereas diffusion models achieve a superior performance ceiling, suggesting that strict sequential ordering may limit the upper bounds of generation quality. Finally, we extend our analysis by adapting Representation Alignment (REPA) to AR models, yielding LlamaGen-REPA. Codes is available at https://github.com/Tencent-Hunyuan/iFSQ

The total variation (TV)-seminorm is considered for piecewise polynomial, globally discontinuous (DG) and continuous (CG) finite element functions on simplicial meshes. A novel, discrete variant (DTV) based on a nodal quadrature formula is defined. DTV has favorable properties, compared to the original TV-seminorm for finite element functions. These include a convenient dual representation in terms of the supremum over the space of Raviart--Thomas finite element functions, subject to a set of simple constraints. It can therefore be shown that a variety of algorithms for classical image reconstruction problems, including TV-L^2 and TV-L^1, can be implemented in low and higher-order finite element spaces with the same efficiency as their counterparts originally developed for images on Cartesian grids.

The field of texture synthesis has witnessed important progresses over the last years, most notably through the use of Convolutional Neural Networks. However, neural synthesis methods still struggle to reproduce large scale structures, especially with high resolution textures. To address this issue, we first introduce a simple multi-resolution framework that efficiently accounts for long-range dependency. Then, we show that additional statistical constraints further improve the reproduction of textures with strong regularity. This can be achieved by constraining both the Gram matrices of a neural network and the power spectrum of the image. Alternatively one may constrain only the autocorrelation of the features of the network and drop the Gram matrices constraints. In an experimental part, the proposed methods are then extensively tested and compared to alternative approaches, both in an unsupervised way and through a user study. Experiments show the interest of the multi-scale scheme for high resolution textures and the interest of combining it with additional constraints for regular textures.

Recent work has shown how denoising and contractive autoencoders implicitly capture the structure of the data-generating density, in the case where the corruption noise is Gaussian, the reconstruction error is the squared error, and the data is continuous-valued. This has led to various proposals for sampling from this implicitly learned density function, using Langevin and Metropolis-Hastings MCMC. However, it remained unclear how to connect the training procedure of regularized auto-encoders to the implicit estimation of the underlying data-generating distribution when the data are discrete, or using other forms of corruption process and reconstruction errors. Another issue is the mathematical justification which is only valid in the limit of small corruption noise. We propose here a different attack on the problem, which deals with all these issues: arbitrary (but noisy enough) corruption, arbitrary reconstruction loss (seen as a log-likelihood), handling both discrete and continuous-valued variables, and removing the bias due to non-infinitesimal corruption noise (or non-infinitesimal contractive penalty).

Reconstructing editable Computer-Aided Design (CAD) models from images is essential for downstream modification, manufacturing, and design reuse. However, existing image-to-CAD methods are developed predominantly on synthetic renderings and face two coupled obstacles: a substantial appearance domain gap between synthetic and real images, and a previously overlooked parameter bias in widely used CAD data. We show that the local normalization adopted by DeepCAD concentrates several geometric parameters around a few discrete values while encoding substantial information in a single scale factor. Consequently, a model can achieve deceptively high parameter accuracy by exploiting these frequent values rather than inferring geometry from the input image. In this paper, we propose RealCAD, a unified framework that addresses these limitations at the representation, image, and feature levels. At the representation level, we redistribute scale information to the corresponding geometric parameters, producing less concentrated parameter distributions in a shared scale space. At the image level, geometry-constrained translation converts synthetic renderings toward the real-image domain while conditioning on object contours. At the feature level, a multi-positive contrastive objective aligns representations of the same CAD model across viewpoints and image domains, enabling CAD sequence prediction from each individual view. We further introduce OpenRealCAD, comprising four-view photographs of 392 3D-printed objects paired with ground-truth command sequences. Experiments show that the revised representation substantially reduces the accuracy attainable from parameter-frequency priors, making parameter accuracy a more reliable measure of image-conditioned geometric inference. RealCAD further improves real-domain command and parameter accuracy, while retaining competitive synthetic-domain performance.

Scientific datasets present unique challenges for machine learning-driven compression methods, including more stringent requirements on accuracy and mitigation of potential invalidating artifacts. Drawing on results from compressed sensing and rate-distortion theory, we introduce effective data compression methods by developing autoencoders using high dimensional latent spaces that are L^1-regularized to obtain sparse low dimensional representations. We show how these information-rich latent spaces can be used to mitigate blurring and other artifacts to obtain highly effective data compression methods for scientific data. We demonstrate our methods for short angle scattering (SAS) datasets showing they can achieve compression ratios around two orders of magnitude and in some cases better. Our compression methods show promise for use in addressing current bottlenecks in transmission, storage, and analysis in high-performance distributed computing environments. This is central to processing the large volume of SAS data being generated at shared experimental facilities around the world to support scientific investigations. Our approaches provide general ways for obtaining specialized compression methods for targeted scientific datasets.

The flat lensless camera design reduces the camera size and weight significantly. In this design, the camera lens is replaced by another optical element that interferes with the incoming light. The image is recovered from the raw sensor measurements using a reconstruction algorithm. Yet, the quality of the reconstructed images is not satisfactory. To mitigate this, we propose utilizing a pre-trained diffusion model with a control network and a learned separable transformation for reconstruction. This allows us to build a prototype flat camera with high-quality imaging, presenting state-of-the-art results in both terms of quality and perceptuality. We demonstrate its ability to leverage also textual descriptions of the captured scene to further enhance reconstruction. Our reconstruction method which leverages the strong capabilities of a pre-trained diffusion model can be used in other imaging systems for improved reconstruction results.

Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map measurements to medical images, leveraging a training dataset of paired images and measurements. These measurements are typically synthesized from images using a fixed physical model of the measurement process, which hinders the generalization capability of models to unknown measurement processes. To address this issue, we propose a fully unsupervised technique for inverse problem solving, leveraging the recently introduced score-based generative models. Specifically, we first train a score-based generative model on medical images to capture their prior distribution. Given measurements and a physical model of the measurement process at test time, we introduce a sampling method to reconstruct an image consistent with both the prior and the observed measurements. Our method does not assume a fixed measurement process during training, and can thus be flexibly adapted to different measurement processes at test time. Empirically, we observe comparable or better performance to supervised learning techniques in several medical imaging tasks in CT and MRI, while demonstrating significantly better generalization to unknown measurement processes.

We view the reconstruction of CAD models in the boundary representation (B-Rep) as the detection of geometric primitives of different orders, i.e. vertices, edges and surface patches, and the correspondence of primitives, which are holistically modeled as a chain complex, and show that by modeling such comprehensive structures more complete and regularized reconstructions can be achieved. We solve the complex generation problem in two steps. First, we propose a novel neural framework that consists of a sparse CNN encoder for input point cloud processing and a tri-path transformer decoder for generating geometric primitives and their mutual relationships with estimated probabilities. Second, given the probabilistic structure predicted by the neural network, we recover a definite B-Rep chain complex by solving a global optimization maximizing the likelihood under structural validness constraints and applying geometric refinements. Extensive tests on large scale CAD datasets demonstrate that the modeling of B-Rep chain complex structure enables more accurate detection for learning and more constrained reconstruction for optimization, leading to structurally more faithful and complete CAD B-Rep models than previous results.

The rapid advancement of diffusion models has significantly improved high-quality image generation, making generated content increasingly challenging to distinguish from real images and raising concerns about potential misuse. In this paper, we observe that diffusion models struggle to accurately reconstruct mid-band frequency information in real images, suggesting the limitation could serve as a cue for detecting diffusion model generated images. Motivated by this observation, we propose a novel method called Frequency-guided Reconstruction Error (FIRE), which, to the best of our knowledge, is the first to investigate the influence of frequency decomposition on reconstruction error. FIRE assesses the variation in reconstruction error before and after the frequency decomposition, offering a robust method for identifying diffusion model generated images. Extensive experiments show that FIRE generalizes effectively to unseen diffusion models and maintains robustness against diverse perturbations.

Recent advances in neural reconstruction using posed image sequences have made remarkable progress. However, due to the lack of depth information, existing volumetric-based techniques simply duplicate 2D image features of the object surface along the entire camera ray. We contend this duplication introduces noise in empty and occluded spaces, posing challenges for producing high-quality 3D geometry. Drawing inspiration from traditional multi-view stereo methods, we propose an end-to-end 3D neural reconstruction framework CVRecon, designed to exploit the rich geometric embedding in the cost volumes to facilitate 3D geometric feature learning. Furthermore, we present Ray-contextual Compensated Cost Volume (RCCV), a novel 3D geometric feature representation that encodes view-dependent information with improved integrity and robustness. Through comprehensive experiments, we demonstrate that our approach significantly improves the reconstruction quality in various metrics and recovers clear fine details of the 3D geometries. Our extensive ablation studies provide insights into the development of effective 3D geometric feature learning schemes. Project page: https://cvrecon.ziyue.cool/