Daily Papers

Recovering high-quality 3D scenes from a single RGB image is a challenging task in computer graphics. Current methods often struggle with domain-specific limitations or low-quality object generation. To address these, we propose CAST (Component-Aligned 3D Scene Reconstruction from a Single RGB Image), a novel method for 3D scene reconstruction and recovery. CAST starts by extracting object-level 2D segmentation and relative depth information from the input image, followed by using a GPT-based model to analyze inter-object spatial relationships. This enables the understanding of how objects relate to each other within the scene, ensuring more coherent reconstruction. CAST then employs an occlusion-aware large-scale 3D generation model to independently generate each object's full geometry, using MAE and point cloud conditioning to mitigate the effects of occlusions and partial object information, ensuring accurate alignment with the source image's geometry and texture. To align each object with the scene, the alignment generation model computes the necessary transformations, allowing the generated meshes to be accurately placed and integrated into the scene's point cloud. Finally, CAST incorporates a physics-aware correction step that leverages a fine-grained relation graph to generate a constraint graph. This graph guides the optimization of object poses, ensuring physical consistency and spatial coherence. By utilizing Signed Distance Fields (SDF), the model effectively addresses issues such as occlusions, object penetration, and floating objects, ensuring that the generated scene accurately reflects real-world physical interactions. CAST can be leveraged in robotics, enabling efficient real-to-simulation workflows and providing realistic, scalable simulation environments for robotic systems.

Artificial Intelligence (AI) weather prediction (AIWP) models are powerful tools for medium-range forecasts but often lack physical consistency, leading to outputs that violate conservation laws. This study introduces a set of novel physics-based schemes designed to enforce the conservation of global dry air mass, moisture budget, and total atmospheric energy in AIWP models. The schemes are highly modular, allowing for seamless integration into a wide range of AI model architectures. Forecast experiments are conducted to demonstrate the benefit of conservation schemes using FuXi, an example AIWP model, modified and adapted for 1.0-degree grid spacing. Verification results show that the conservation schemes can guide the model in producing forecasts that obey conservation laws. The forecast skills of upper-air and surface variables are also improved, with longer forecast lead times receiving larger benefits. Notably, large performance gains are found in the total precipitation forecasts, owing to the reduction of drizzle bias. The proposed conservation schemes establish a foundation for implementing other physics-based schemes in the future. They also provide a new way to integrate atmospheric domain knowledge into the design and refinement of AIWP models.

Novel view synthesis from a single image requires inferring occluded regions of objects and scenes whilst simultaneously maintaining semantic and physical consistency with the input. Existing approaches condition neural radiance fields (NeRF) on local image features, projecting points to the input image plane, and aggregating 2D features to perform volume rendering. However, under severe occlusion, this projection fails to resolve uncertainty, resulting in blurry renderings that lack details. In this work, we propose NerfDiff, which addresses this issue by distilling the knowledge of a 3D-aware conditional diffusion model (CDM) into NeRF through synthesizing and refining a set of virtual views at test time. We further propose a novel NeRF-guided distillation algorithm that simultaneously generates 3D consistent virtual views from the CDM samples, and finetunes the NeRF based on the improved virtual views. Our approach significantly outperforms existing NeRF-based and geometry-free approaches on challenging datasets, including ShapeNet, ABO, and Clevr3D.

Existing ML-based atmospheric models are not suitable for climate prediction, which requires long-term stability and physical consistency. We present ACE (AI2 Climate Emulator), a 200M-parameter, autoregressive machine learning emulator of an existing comprehensive 100-km resolution global atmospheric model. The formulation of ACE allows evaluation of physical laws such as the conservation of mass and moisture. The emulator is stable for 100 years, nearly conserves column moisture without explicit constraints and faithfully reproduces the reference model's climate, outperforming a challenging baseline on over 90% of tracked variables. ACE requires nearly 100x less wall clock time and is 100x more energy efficient than the reference model using typically available resources. Without fine-tuning, ACE can stably generalize to a previously unseen historical sea surface temperature dataset.

With the rapid development of diffusion models, text-to-image(T2I) models have made significant progress, showcasing impressive abilities in prompt following and image generation. Recently launched models such as FLUX.1 and Ideogram2.0, along with others like Dall-E3 and Stable Diffusion 3, have demonstrated exceptional performance across various complex tasks, raising questions about whether T2I models are moving towards general-purpose applicability. Beyond traditional image generation, these models exhibit capabilities across a range of fields, including controllable generation, image editing, video, audio, 3D, and motion generation, as well as computer vision tasks like semantic segmentation and depth estimation. However, current evaluation frameworks are insufficient to comprehensively assess these models' performance across expanding domains. To thoroughly evaluate these models, we developed the IMAGINE-E and tested six prominent models: FLUX.1, Ideogram2.0, Midjourney, Dall-E3, Stable Diffusion 3, and Jimeng. Our evaluation is divided into five key domains: structured output generation, realism, and physical consistency, specific domain generation, challenging scenario generation, and multi-style creation tasks. This comprehensive assessment highlights each model's strengths and limitations, particularly the outstanding performance of FLUX.1 and Ideogram2.0 in structured and specific domain tasks, underscoring the expanding applications and potential of T2I models as foundational AI tools. This study provides valuable insights into the current state and future trajectory of T2I models as they evolve towards general-purpose usability. Evaluation scripts will be released at https://github.com/jylei16/Imagine-e.

Decomposing physically-based materials from images into their constituent properties remains challenging, particularly when maintaining both computational efficiency and physical consistency. While recent diffusion-based approaches have shown promise, they face substantial computational overhead due to multiple denoising steps and separate models for different material properties. We present SuperMat, a single-step framework that achieves high-quality material decomposition with one-step inference. This enables end-to-end training with perceptual and re-render losses while decomposing albedo, metallic, and roughness maps at millisecond-scale speeds. We further extend our framework to 3D objects through a UV refinement network, enabling consistent material estimation across viewpoints while maintaining efficiency. Experiments demonstrate that SuperMat achieves state-of-the-art PBR material decomposition quality while reducing inference time from seconds to milliseconds per image, and completes PBR material estimation for 3D objects in approximately 3 seconds. The project page is at https://hyj542682306.github.io/SuperMat/.

The generation of industrial Computer-Aided Design (CAD) models from user requests and specifications is crucial to enhancing efficiency in modern manufacturing. Traditional methods of CAD generation rely heavily on manual inputs and struggle with complex or non-standard designs, making them less suited for dynamic industrial needs. To overcome these challenges, we introduce Text2CAD, a novel framework that employs stable diffusion models tailored to automate the generation process and efficiently bridge the gap between user specifications in text and functional CAD models. This approach directly translates the user's textural descriptions into detailed isometric images, which are then precisely converted into orthographic views, e.g., top, front, and side, providing sufficient information to reconstruct 3D CAD models. This process not only streamlines the creation of CAD models from textual descriptions but also ensures that the resulting models uphold physical and dimensional consistency essential for practical engineering applications. Our experimental results show that Text2CAD effectively generates technical drawings that are accurately translated into high-quality 3D CAD models, showing substantial potential to revolutionize CAD automation in response to user demands.

We present a novel video generation framework that integrates 3-dimensional geometry and dynamic awareness. To achieve this, we augment 2D videos with 3D point trajectories and align them in pixel space. The resulting 3D-aware video dataset, PointVid, is then used to fine-tune a latent diffusion model, enabling it to track 2D objects with 3D Cartesian coordinates. Building on this, we regularize the shape and motion of objects in the video to eliminate undesired artifacts, \eg, nonphysical deformation. Consequently, we enhance the quality of generated RGB videos and alleviate common issues like object morphing, which are prevalent in current video models due to a lack of shape awareness. With our 3D augmentation and regularization, our model is capable of handling contact-rich scenarios such as task-oriented videos. These videos involve complex interactions of solids, where 3D information is essential for perceiving deformation and contact. Furthermore, our model improves the overall quality of video generation by promoting the 3D consistency of moving objects and reducing abrupt changes in shape and motion.

AI is revolutionizing MRI along the acquisition and processing chain. Advanced AI frameworks have been developed to apply AI in various successive tasks, such as image reconstruction, quantitative parameter map estimation, and image segmentation. Existing frameworks are often designed to perform tasks independently or are focused on specific models or datasets, limiting generalization. We introduce ATOMMIC, an open-source toolbox that streamlines AI applications for accelerated MRI reconstruction and analysis. ATOMMIC implements several tasks using DL networks and enables MultiTask Learning (MTL) to perform related tasks integrated, targeting generalization in the MRI domain. We first review the current state of AI frameworks for MRI through a comprehensive literature search and by parsing 12,479 GitHub repositories. We benchmark 25 DL models on eight publicly available datasets to present distinct applications of ATOMMIC on accelerated MRI reconstruction, image segmentation, quantitative parameter map estimation, and joint accelerated MRI reconstruction and image segmentation utilizing MTL. Our findings demonstrate that ATOMMIC is the only MTL framework with harmonized complex-valued and real-valued data support. Evaluations on single tasks show that physics-based models, which enforce data consistency by leveraging the physical properties of MRI, outperform other models in reconstructing highly accelerated acquisitions. Physics-based models that produce high reconstruction quality can accurately estimate quantitative parameter maps. When high-performing reconstruction models are combined with robust segmentation networks utilizing MTL, performance is improved in both tasks. ATOMMIC facilitates MRI reconstruction and analysis by standardizing workflows, enhancing data interoperability, integrating unique features like MTL, and effectively benchmarking DL models.

Diffusion models (DMs) have enabled breakthroughs in image synthesis tasks but lack an intuitive interface for consistent image-to-image (I2I) translation. Various methods have been explored to address this issue, including mask-based methods, attention-based methods, and image-conditioning. However, it remains a critical challenge to enable unpaired I2I translation with pre-trained DMs while maintaining satisfying consistency. This paper introduces Cyclenet, a novel but simple method that incorporates cycle consistency into DMs to regularize image manipulation. We validate Cyclenet on unpaired I2I tasks of different granularities. Besides the scene and object level translation, we additionally contribute a multi-domain I2I translation dataset to study the physical state changes of objects. Our empirical studies show that Cyclenet is superior in translation consistency and quality, and can generate high-quality images for out-of-domain distributions with a simple change of the textual prompt. Cyclenet is a practical framework, which is robust even with very limited training data (around 2k) and requires minimal computational resources (1 GPU) to train. Project homepage: https://cyclenetweb.github.io/

Recent advances in text-to-video generation have harnessed the power of diffusion models to create visually compelling content conditioned on text prompts. However, they usually encounter high computational costs and often struggle to produce videos with coherent physical motions. To tackle these issues, we propose GPT4Motion, a training-free framework that leverages the planning capability of large language models such as GPT, the physical simulation strength of Blender, and the excellent image generation ability of text-to-image diffusion models to enhance the quality of video synthesis. Specifically, GPT4Motion employs GPT-4 to generate a Blender script based on a user textual prompt, which commands Blender's built-in physics engine to craft fundamental scene components that encapsulate coherent physical motions across frames. Then these components are inputted into Stable Diffusion to generate a video aligned with the textual prompt. Experimental results on three basic physical motion scenarios, including rigid object drop and collision, cloth draping and swinging, and liquid flow, demonstrate that GPT4Motion can generate high-quality videos efficiently in maintaining motion coherency and entity consistency. GPT4Motion offers new insights in text-to-video research, enhancing its quality and broadening its horizon for future explorations.

Generating dense multiview images from text prompts is crucial for creating high-fidelity 3D assets. Nevertheless, existing methods struggle with space-view correspondences, resulting in sparse and low-quality outputs. In this paper, we introduce CoSER, a novel consistent dense Multiview Text-to-Image Generator for Text-to-3D, achieving both efficiency and quality by meticulously learning neighbor-view coherence and further alleviating ambiguity through the swift traversal of all views. For achieving neighbor-view consistency, each viewpoint densely interacts with adjacent viewpoints to perceive the global spatial structure, and aggregates information along motion paths explicitly defined by physical principles to refine details. To further enhance cross-view consistency and alleviate content drift, CoSER rapidly scan all views in spiral bidirectional manner to aware holistic information and then scores each point based on semantic material. Subsequently, we conduct weighted down-sampling along the spatial dimension based on scores, thereby facilitating prominent information fusion across all views with lightweight computation. Technically, the core module is built by integrating the attention mechanism with a selective state space model, exploiting the robust learning capabilities of the former and the low overhead of the latter. Extensive evaluation shows that CoSER is capable of producing dense, high-fidelity, content-consistent multiview images that can be flexibly integrated into various 3D generation models.

Artificial neural networks have become a staple computing technique in many fields. Yet, they present fundamental differences with classical computing hardware in the way they process information. Photonic implementations of neural network architectures potentially offer fundamental advantages over their electronic counterparts in terms of speed, processing parallelism, scalability and energy efficiency. Scalable and high performance photonic neural networks (PNNs) have been demonstrated, yet they remain scarce. In this work, we study the performance of such a scalable, fully parallel and autonomous PNN based on a large area vertical-cavity surface-emitting laser (LA-VCSEL). We show how the performance varies with different physical parameters, namely, injection wavelength, injection power, and bias current. Furthermore, we link these physical parameters to the general computational measures of consistency and dimensionality. We present a general method of gauging dimensionality in high dimensional nonlinear systems subject to noise, which could be applied to many systems in the context of neuromorphic computing. Our work will inform future implementations of spatially multiplexed VCSEL PNNs.

3D Gaussian Splatting has demonstrated notable success in large-scale scene reconstruction, but challenges persist due to high training memory consumption and storage overhead. Hybrid representations that integrate implicit and explicit features offer a way to mitigate these limitations. However, when applied in parallelized block-wise training, two critical issues arise since reconstruction accuracy deteriorates due to reduced data diversity when training each block independently, and parallel training restricts the number of divided blocks to the available number of GPUs. To address these issues, we propose Momentum-GS, a novel approach that leverages momentum-based self-distillation to promote consistency and accuracy across the blocks while decoupling the number of blocks from the physical GPU count. Our method maintains a teacher Gaussian decoder updated with momentum, ensuring a stable reference during training. This teacher provides each block with global guidance in a self-distillation manner, promoting spatial consistency in reconstruction. To further ensure consistency across the blocks, we incorporate block weighting, dynamically adjusting each block's weight according to its reconstruction accuracy. Extensive experiments on large-scale scenes show that our method consistently outperforms existing techniques, achieving a 12.8% improvement in LPIPS over CityGaussian with much fewer divided blocks and establishing a new state of the art. Project page: https://jixuan-fan.github.io/Momentum-GS_Page/

The growing capabilities of AI in generating video content have brought forward significant challenges in effectively evaluating these videos. Unlike static images or text, video content involves complex spatial and temporal dynamics which may require a more comprehensive and systematic evaluation of its contents in aspects like video presentation quality, semantic information delivery, alignment with human intentions, and the virtual-reality consistency with our physical world. This survey identifies the emerging field of AI-Generated Video Evaluation (AIGVE), highlighting the importance of assessing how well AI-generated videos align with human perception and meet specific instructions. We provide a structured analysis of existing methodologies that could be potentially used to evaluate AI-generated videos. By outlining the strengths and gaps in current approaches, we advocate for the development of more robust and nuanced evaluation frameworks that can handle the complexities of video content, which include not only the conventional metric-based evaluations, but also the current human-involved evaluations, and the future model-centered evaluations. This survey aims to establish a foundational knowledge base for both researchers from academia and practitioners from the industry, facilitating the future advancement of evaluation methods for AI-generated video content.

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate high-quality samples with fewer function evaluations, typically through iterative rectification methods or optimal transport solutions. In this paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Consistency-FM directly defines straight flows starting from different times to the same endpoint, imposing constraints on their velocity values. Additionally, we propose a multi-segment training approach for Consistency-FM to enhance expressiveness, achieving a better trade-off between sampling quality and speed. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models and 1.7x faster than rectified flow models while achieving better generation quality. Our code is available at: https://github.com/YangLing0818/consistency_flow_matching

Machine Learning methods can learn how to reconstruct Magnetic Resonance Images and thereby accelerate acquisition, which is of paramount importance to the clinical workflow. Physics-informed networks incorporate the forward model of accelerated MRI reconstruction in the learning process. With increasing network complexity, robustness is not ensured when reconstructing data unseen during training. We aim to embed data consistency (DC) in deep networks while balancing the degree of network complexity. While doing so, we will assess whether either explicit or implicit enforcement of DC in varying network architectures is preferred to optimize performance. We propose a scheme called Cascades of Independently Recurrent Inference Machines (CIRIM) to assess DC through unrolled optimization. Herein we assess DC both implicitly by gradient descent and explicitly by a designed term. Extensive comparison of the CIRIM to CS as well as to other methods is performed: the E2EVN, CascadeNet, KIKINet, LPDNet, RIM, IRIM, and UNet. Models were trained and evaluated on T1-weighted and FLAIR contrast brain data, and T2-weighted knee data. Both 1D and 2D undersampling patterns were evaluated. Robustness was tested by reconstructing 7.5x prospectively undersampled 3D FLAIR MRI data of Multiple Sclerosis (MS) patients with white matter lesions. The CIRIM performed best when implicitly enforcing DC, while the E2EVN required an explicit DC formulation. In reconstructing MS patient data, prospectively acquired with a sampling pattern unseen during model training, the CIRIM maintained lesion contrast while efficiently denoising the images. The CIRIM showed highly promising generalization capabilities maintaining a very fair trade-off between reconstructed image quality and fast reconstruction times, which is crucial in the clinical workflow.

The image-to-image translation abilities of generative learning models have recently made significant progress in the estimation of complex (steered) mappings between image distributions. While appearance based tasks like image in-painting or style transfer have been studied at length, we propose to investigate the potential of generative models in the context of physical simulations. Providing a dataset of 300k image-pairs and baseline evaluations for three different physical simulation tasks, we propose a benchmark to investigate the following research questions: i) are generative models able to learn complex physical relations from input-output image pairs? ii) what speedups can be achieved by replacing differential equation based simulations? While baseline evaluations of different current models show the potential for high speedups (ii), these results also show strong limitations toward the physical correctness (i). This underlines the need for new methods to enforce physical correctness. Data, baseline models and evaluation code http://www.physics-gen.org.

All current formulations of thermodynamics invoke some form of coarse-graining or ensembles as the supposed link between their own laws and the microscopic laws of motion. They deal only with ensemble-averages, expectation values, macroscopic limits, infinite heat baths, etc., not with the details of physical variables of individual microscopic systems. They are consistent with the laws of motion for finite systems only in certain approximations, which improve with increasing scale, given various assumptions about initial conditions which are neither specified precisely nor even thought to hold exactly in nature. Here I propose a new formulation of the zeroth, first and second laws, improving upon the axiomatic approach to thermodynamics (Carath\'eodory, 1909; Lieb & Yngvason, 1999), via the principles of the recently proposed constructor theory. Specifically, I provide a non-approximative, scale-independent formulation of 'adiabatic accessibility'; this in turn provides a non-approximative, scale-independent distinction between work and heat and reveals an unexpected connection between information theory and the first law of thermodynamics (not just the second). It also achieves the long-sought unification of the axiomatic approach with Kelvin's.

The recently developed Sora model [1] has exhibited remarkable capabilities in video generation, sparking intense discussions regarding its ability to simulate real-world phenomena. Despite its growing popularity, there is a lack of established metrics to evaluate its fidelity to real-world physics quantitatively. In this paper, we introduce a new benchmark that assesses the quality of the generated videos based on their adherence to real-world physics principles. We employ a method that transforms the generated videos into 3D models, leveraging the premise that the accuracy of 3D reconstruction is heavily contingent on the video quality. From the perspective of 3D reconstruction, we use the fidelity of the geometric constraints satisfied by the constructed 3D models as a proxy to gauge the extent to which the generated videos conform to real-world physics rules. Project page: https://sora-geometrical-consistency.github.io/

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.

Consistency models (CMs) are a powerful class of diffusion-based generative models optimized for fast sampling. Most existing CMs are trained using discretized timesteps, which introduce additional hyperparameters and are prone to discretization errors. While continuous-time formulations can mitigate these issues, their success has been limited by training instability. To address this, we propose a simplified theoretical framework that unifies previous parameterizations of diffusion models and CMs, identifying the root causes of instability. Based on this analysis, we introduce key improvements in diffusion process parameterization, network architecture, and training objectives. These changes enable us to train continuous-time CMs at an unprecedented scale, reaching 1.5B parameters on ImageNet 512x512. Our proposed training algorithm, using only two sampling steps, achieves FID scores of 2.06 on CIFAR-10, 1.48 on ImageNet 64x64, and 1.88 on ImageNet 512x512, narrowing the gap in FID scores with the best existing diffusion models to within 10%.

AI video generation is undergoing a revolution, with quality and realism advancing rapidly. These advances have led to a passionate scientific debate: Do video models learn ``world models'' that discover laws of physics -- or, alternatively, are they merely sophisticated pixel predictors that achieve visual realism without understanding the physical principles of reality? We address this question by developing Physics-IQ, a comprehensive benchmark dataset that can only be solved by acquiring a deep understanding of various physical principles, like fluid dynamics, optics, solid mechanics, magnetism and thermodynamics. We find that across a range of current models (Sora, Runway, Pika, Lumiere, Stable Video Diffusion, and VideoPoet), physical understanding is severely limited, and unrelated to visual realism. At the same time, some test cases can already be successfully solved. This indicates that acquiring certain physical principles from observation alone may be possible, but significant challenges remain. While we expect rapid advances ahead, our work demonstrates that visual realism does not imply physical understanding. Our project page is at https://physics-iq.github.io; code at https://github.com/google-deepmind/physics-IQ-benchmark.

Deep neural networks have enabled improved image quality and fast inference times for various inverse problems, including accelerated magnetic resonance imaging (MRI) reconstruction. However, such models require a large number of fully-sampled ground truth datasets, which are difficult to curate, and are sensitive to distribution drifts. In this work, we propose applying physics-driven data augmentations for consistency training that leverage our domain knowledge of the forward MRI data acquisition process and MRI physics to achieve improved label efficiency and robustness to clinically-relevant distribution drifts. Our approach, termed VORTEX, (1) demonstrates strong improvements over supervised baselines with and without data augmentation in robustness to signal-to-noise ratio change and motion corruption in data-limited regimes; (2) considerably outperforms state-of-the-art purely image-based data augmentation techniques and self-supervised reconstruction methods on both in-distribution and out-of-distribution data; and (3) enables composing heterogeneous image-based and physics-driven data augmentations. Our code is available at https://github.com/ad12/meddlr.

Existing methods for the 4D reconstruction of general, non-rigidly deforming objects focus on novel-view synthesis and neglect correspondences. However, time consistency enables advanced downstream tasks like 3D editing, motion analysis, or virtual-asset creation. We propose SceNeRFlow to reconstruct a general, non-rigid scene in a time-consistent manner. Our dynamic-NeRF method takes multi-view RGB videos and background images from static cameras with known camera parameters as input. It then reconstructs the deformations of an estimated canonical model of the geometry and appearance in an online fashion. Since this canonical model is time-invariant, we obtain correspondences even for long-term, long-range motions. We employ neural scene representations to parametrize the components of our method. Like prior dynamic-NeRF methods, we use a backwards deformation model. We find non-trivial adaptations of this model necessary to handle larger motions: We decompose the deformations into a strongly regularized coarse component and a weakly regularized fine component, where the coarse component also extends the deformation field into the space surrounding the object, which enables tracking over time. We show experimentally that, unlike prior work that only handles small motion, our method enables the reconstruction of studio-scale motions.

In recent years, there has been rapid development in 3D generation models, opening up new possibilities for applications such as simulating the dynamic movements of 3D objects and customizing their behaviors. However, current 3D generative models tend to focus only on surface features such as color and shape, neglecting the inherent physical properties that govern the behavior of objects in the real world. To accurately simulate physics-aligned dynamics, it is essential to predict the physical properties of materials and incorporate them into the behavior prediction process. Nonetheless, predicting the diverse materials of real-world objects is still challenging due to the complex nature of their physical attributes. In this paper, we propose Physics3D, a novel method for learning various physical properties of 3D objects through a video diffusion model. Our approach involves designing a highly generalizable physical simulation system based on a viscoelastic material model, which enables us to simulate a wide range of materials with high-fidelity capabilities. Moreover, we distill the physical priors from a video diffusion model that contains more understanding of realistic object materials. Extensive experiments demonstrate the effectiveness of our method with both elastic and plastic materials. Physics3D shows great potential for bridging the gap between the physical world and virtual neural space, providing a better integration and application of realistic physical principles in virtual environments. Project page: https://liuff19.github.io/Physics3D.

Imposing known physical constraints, such as conservation laws, during neural network training introduces an inductive bias that can improve accuracy, reliability, convergence, and data efficiency for modeling physical dynamics. While such constraints can be softly imposed via loss function penalties, recent advancements in differentiable physics and optimization improve performance by incorporating PDE-constrained optimization as individual layers in neural networks. This enables a stricter adherence to physical constraints. However, imposing hard constraints significantly increases computational and memory costs, especially for complex dynamical systems. This is because it requires solving an optimization problem over a large number of points in a mesh, representing spatial and temporal discretizations, which greatly increases the complexity of the constraint. To address this challenge, we develop a scalable approach to enforce hard physical constraints using Mixture-of-Experts (MoE), which can be used with any neural network architecture. Our approach imposes the constraint over smaller decomposed domains, each of which is solved by an "expert" through differentiable optimization. During training, each expert independently performs a localized backpropagation step by leveraging the implicit function theorem; the independence of each expert allows for parallelization across multiple GPUs. Compared to standard differentiable optimization, our scalable approach achieves greater accuracy in the neural PDE solver setting for predicting the dynamics of challenging non-linear systems. We also improve training stability and require significantly less computation time during both training and inference stages.

In this article, we study the consistency of the template estimation with the Fr\'echet mean in quotient spaces. The Fr\'echet mean in quotient spaces is often used when the observations are deformed or transformed by a group action. We show that in most cases this estimator is actually inconsistent. We exhibit a sufficient condition for this inconsistency, which amounts to the folding of the distribution of the noisy template when it is projected to the quotient space. This condition appears to be fulfilled as soon as the support of the noise is large enough. To quantify this inconsistency we provide lower and upper bounds of the bias as a function of the variability (the noise level). This shows that the consistency bias cannot be neglected when the variability increases.