Nicholas Sharp

Tianchang Shen, Jacob Munkberg, Jon Hasselgren et al. · nvidia, utoronto

This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry, generative modeling, and inverse physics. Existing implementations adapt classic isosurface extraction algorithms like Marching Cubes or Dual Contouring; these techniques were designed to extract meshes from fixed, known fields, and in the optimization setting they lack the degrees of freedom to represent high-quality feature-preserving meshes, or suffer from numerical instabilities. We introduce FlexiCubes, an isosurface representation specifically designed for optimizing an unknown mesh with respect to geometric, visual, or even physical objectives. Our main insight is to introduce additional carefully-chosen parameters into the representation, which allow local flexible adjustments to the extracted mesh geometry and connectivity. These parameters are updated along with the underlying scalar field via automatic differentiation when optimizing for a downstream task. We base our extraction scheme on Dual Marching Cubes for improved topological properties, and present extensions to optionally generate tetrahedral and hierarchically-adaptive meshes. Extensive experiments validate FlexiCubes on both synthetic benchmarks and real-world applications, showing that it offers significant improvements in mesh quality and geometric fidelity.

Jonathan Lorraine, Kevin Xie, Xiaohui Zeng et al. · nvidia, utoronto

Text-to-3D modelling has seen exciting progress by combining generative text-to-image models with image-to-3D methods like Neural Radiance Fields. DreamFusion recently achieved high-quality results but requires a lengthy, per-prompt optimization to create 3D objects. To address this, we amortize optimization over text prompts by training on many prompts simultaneously with a unified model, instead of separately. With this, we share computation across a prompt set, training in less time than per-prompt optimization. Our framework - Amortized text-to-3D (ATT3D) - enables knowledge-sharing between prompts to generalize to unseen setups and smooth interpolations between text for novel assets and simple animations.

Donglai Xiang, Vismay Modi, Rishit Dagli et al.

We present a novel formulation for mesh-free, reduced-order simulation of deformable hyperelastic objects. Existing work in reduced-order elastodynamic simulation represents the input geometry by either meshes, which can be difficult to obtain due to challenges in scanning and triangulating complex shapes, or by neural fields that require per-shape optimization. We propose to adopt a Reproducing Kernel Particle Method (RKPM) representation, which enables the construction of reduced-order skinning weights by solving a generalized eigensystem on the Hessian matrix of the elastic energy. We demonstrate that this formulation not only leads to a 40x training speedup compared with the per-shape optimization of neural fields, but also achieves lower simulation error when evaluated against the converged results of finite element method. We show our simulation results on a wide variety of objects in different representations including meshes and Gaussian splats, as well as the application of our method in the downstream task of robot simulation.

Zian Wang, Tianchang Shen, Merlin Nimier-David et al. · nvidia, utoronto

Neural radiance fields achieve unprecedented quality for novel view synthesis, but their volumetric formulation remains expensive, requiring a huge number of samples to render high-resolution images. Volumetric encodings are essential to represent fuzzy geometry such as foliage and hair, and they are well-suited for stochastic optimization. Yet, many scenes ultimately consist largely of solid surfaces which can be accurately rendered by a single sample per pixel. Based on this insight, we propose a neural radiance formulation that smoothly transitions between volumetric- and surface-based rendering, greatly accelerating rendering speed and even improving visual fidelity. Our method constructs an explicit mesh envelope which spatially bounds a neural volumetric representation. In solid regions, the envelope nearly converges to a surface and can often be rendered with a single sample. To this end, we generalize the NeuS formulation with a learned spatially-varying kernel size which encodes the spread of the density, fitting a wide kernel to volume-like regions and a tight kernel to surface-like regions. We then extract an explicit mesh of a narrow band around the surface, with width determined by the kernel size, and fine-tune the radiance field within this band. At inference time, we cast rays against the mesh and evaluate the radiance field only within the enclosed region, greatly reducing the number of samples required. Experiments show that our approach enables efficient rendering at very high fidelity. We also demonstrate that the extracted envelope enables downstream applications such as animation and simulation.

Tianchang Shen, Sherwin Bahmani, Kai He et al. · nvidia, utoronto

Recent advances in video generation enable a new paradigm for 3D scene creation: generating camera-controlled videos that simulate scene walkthroughs, then lifting them to 3D via feed-forward reconstruction techniques. This generative reconstruction approach combines the visual fidelity and creative capacity of video models with 3D outputs ready for real-time rendering and simulation. Scaling to large, complex environments requires 3D-consistent video generation over long camera trajectories with large viewpoint changes and location revisits, a setting where current video models degrade quickly. Existing methods for long-horizon generation are fundamentally limited by two forms of degradation: spatial forgetting and temporal drifting. As exploration proceeds, previously observed regions fall outside the model's temporal context, forcing the model to hallucinate structures when revisited. Meanwhile, autoregressive generation accumulates small synthesis errors over time, gradually distorting scene appearance and geometry. We present Lyra 2.0, a framework for generating persistent, explorable 3D worlds at scale. To address spatial forgetting, we maintain per-frame 3D geometry and use it solely for information routing -- retrieving relevant past frames and establishing dense correspondences with the target viewpoints -- while relying on the generative prior for appearance synthesis. To address temporal drifting, we train with self-augmented histories that expose the model to its own degraded outputs, teaching it to correct drift rather than propagate it. Together, these enable substantially longer and 3D-consistent video trajectories, which we leverage to fine-tune feed-forward reconstruction models that reliably recover high-quality 3D scenes.

Tianshi Cao, Karsten Kreis, Sanja Fidler et al.

We present TexFusion (Texture Diffusion), a new method to synthesize textures for given 3D geometries, using large-scale text-guided image diffusion models. In contrast to recent works that leverage 2D text-to-image diffusion models to distill 3D objects using a slow and fragile optimization process, TexFusion introduces a new 3D-consistent generation technique specifically designed for texture synthesis that employs regular diffusion model sampling on different 2D rendered views. Specifically, we leverage latent diffusion models, apply the diffusion model's denoiser on a set of 2D renders of the 3D object, and aggregate the different denoising predictions on a shared latent texture map. Final output RGB textures are produced by optimizing an intermediate neural color field on the decodings of 2D renders of the latent texture. We thoroughly validate TexFusion and show that we can efficiently generate diverse, high quality and globally coherent textures. We achieve state-of-the-art text-guided texture synthesis performance using only image diffusion models, while avoiding the pitfalls of previous distillation-based methods. The text-conditioning offers detailed control and we also do not rely on any ground truth 3D textures for training. This makes our method versatile and applicable to a broad range of geometry and texture types. We hope that TexFusion will advance AI-based texturing of 3D assets for applications in virtual reality, game design, simulation, and more.

Tianchang Shen, Zhaoshuo Li, Marc Law et al. · nvidia, utoronto

Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup lacking local structure. This work presents a scheme to directly generate manifold, polygonal meshes of complex connectivity as the output of a neural network. Our key innovation is to define a continuous latent connectivity space at each mesh vertex, which implies the discrete mesh. In particular, our vertex embeddings generate cyclic neighbor relationships in a halfedge mesh representation, which gives a guarantee of edge-manifoldness and the ability to represent general polygonal meshes. This representation is well-suited to machine learning and stochastic optimization, without restriction on connectivity or topology. We first explore the basic properties of this representation, then use it to fit distributions of meshes from large datasets. The resulting models generate diverse meshes with tessellation structure learned from the dataset population, with concise details and high-quality mesh elements. In applications, this approach not only yields high-quality outputs from generative models, but also enables directly learning challenging geometry processing tasks such as mesh repair.

Nicolas Moenne-Loccoz, Ashkan Mirzaei, Or Perel et al.

Particle-based representations of radiance fields such as 3D Gaussian Splatting have found great success for reconstructing and re-rendering of complex scenes. Most existing methods render particles via rasterization, projecting them to screen space tiles for processing in a sorted order. This work instead considers ray tracing the particles, building a bounding volume hierarchy and casting a ray for each pixel using high-performance GPU ray tracing hardware. To efficiently handle large numbers of semi-transparent particles, we describe a specialized rendering algorithm which encapsulates particles with bounding meshes to leverage fast ray-triangle intersections, and shades batches of intersections in depth-order. The benefits of ray tracing are well-known in computer graphics: processing incoherent rays for secondary lighting effects such as shadows and reflections, rendering from highly-distorted cameras common in robotics, stochastically sampling rays, and more. With our renderer, this flexibility comes at little cost compared to rasterization. Experiments demonstrate the speed and accuracy of our approach, as well as several applications in computer graphics and vision. We further propose related improvements to the basic Gaussian representation, including a simple use of generalized kernel functions which significantly reduces particle hit counts.

Selena Ling, Nicholas Sharp, Alec Jacobson

The Adam optimization algorithm has proven remarkably effective for optimization problems across machine learning and even traditional tasks in geometry processing. At the same time, the development of equivariant methods, which preserve their output under the action of rotation or some other transformation, has proven to be important for geometry problems across these domains. In this work, we observe that Adam $-$ when treated as a function that maps initial conditions to optimized results $-$ is not rotation equivariant for vector-valued parameters due to per-coordinate moment updates. This leads to significant artifacts and biases in practice. We propose to resolve this deficiency with VectorAdam, a simple modification which makes Adam rotation-equivariant by accounting for the vector structure of optimization variables. We demonstrate this approach on problems in machine learning and traditional geometric optimization, showing that equivariant VectorAdam resolves the artifacts and biases of traditional Adam when applied to vector-valued data, with equivalent or even improved rates of convergence.

Yuezhi Yang, Qixing Huang, Mikaela Angelina Uy et al.

This work proposes a new formulation to the long-standing problem of convex decomposition through learning feature fields, enabling the first feed-forward model for open-world convex decomposition. Our method produces high-quality decompositions of 3D shapes into a union of convex bodies, which are essential to accelerate collision detection in physical simulation, amongst many other applications. The key insight is to adopt a feature learning approach and learn a continuous feature field that can later be clustered to yield a good convex decomposition via our self-supervised, purely-geometric objective derived from the classical definition of convexity. Our formulation can be used for single shape optimization, but more importantly, feature prediction unlocks scalable, self-supervised learning on large datasets resulting in the first learned open-world model for convex decomposition. Experiments show that our decompositions are higher-quality than alternatives and generalize across open-world objects as well as across representations to meshes, CAD models, and even Gaussian splats. https://research.nvidia.com/labs/sil/projects/learning-convex-decomp/

Minghua Liu, Mikaela Angelina Uy, Donglai Xiang et al.

We propose PartField, a feedforward approach for learning part-based 3D features, which captures the general concept of parts and their hierarchy without relying on predefined templates or text-based names, and can be applied to open-world 3D shapes across various modalities. PartField requires only a 3D feedforward pass at inference time, significantly improving runtime and robustness compared to prior approaches. Our model is trained by distilling 2D and 3D part proposals from a mix of labeled datasets and image segmentations on large unsupervised datasets, via a contrastive learning formulation. It produces a continuous feature field which can be clustered to yield a hierarchical part decomposition. Comparisons show that PartField is up to 20% more accurate and often orders of magnitude faster than other recent class-agnostic part-segmentation methods. Beyond single-shape part decomposition, consistency in the learned field emerges across shapes, enabling tasks such as co-segmentation and correspondence, which we demonstrate in several applications of these general-purpose, hierarchical, and consistent 3D feature fields. Check our Webpage! https://research.nvidia.com/labs/toronto-ai/partfield-release/

Gilles Daviet, Tianchang Shen, Nicholas Sharp et al. · nvidia, utoronto

We present an elastic simulator for domains defined as evolving implicit functions, which is efficient, robust, and differentiable with respect to both shape and material. This simulator is motivated by applications in 3D reconstruction: it is increasingly effective to recover geometry from observed images as implicit functions, but physical applications require accurately simulating and optimizing-for the behavior of such shapes under deformation, which has remained challenging. Our key technical innovation is to train a small neural network to fit quadrature points for robust numerical integration on implicit grid cells. When coupled with a Mixed Finite Element formulation, this yields a smooth, fully differentiable simulation model connecting the evolution of the underlying implicit surface to its elastic response. We demonstrate the efficacy of our approach on forward simulation of implicits, direct simulation of 3D shapes during editing, and novel physics-based shape and topology optimizations in conjunction with differentiable rendering.

Vismay Modi, Nicholas Sharp, Or Perel et al.

The proliferation of 3D representations, from explicit meshes to implicit neural fields and more, motivates the need for simulators agnostic to representation. We present a data-, mesh-, and grid-free solution for elastic simulation for any object in any geometric representation undergoing large, nonlinear deformations. We note that every standard geometric representation can be reduced to an occupancy function queried at any point in space, and we define a simulator atop this common interface. For each object, we fit a small implicit neural network encoding spatially varying weights that act as a reduced deformation basis. These weights are trained to learn physically significant motions in the object via random perturbations. Our loss ensures we find a weight-space basis that best minimizes deformation energy by stochastically evaluating elastic energies through Monte Carlo sampling of the deformation volume. At runtime, we simulate in the reduced basis and sample the deformations back to the original domain. Our experiments demonstrate the versatility, accuracy, and speed of this approach on data including signed distance functions, point clouds, neural primitives, tomography scans, radiance fields, Gaussian splats, surface meshes, and volume meshes, as well as showing a variety of material energies, contact models, and time integration schemes.

Nicholas Sharp, Cristian Romero, Alec Jacobson et al.

Physical systems ranging from elastic bodies to kinematic linkages are defined on high-dimensional configuration spaces, yet their typical low-energy configurations are concentrated on much lower-dimensional subspaces. This work addresses the challenge of identifying such subspaces automatically: given as input an energy function for a high-dimensional system, we produce a low-dimensional map whose image parameterizes a diverse yet low-energy submanifold of configurations. The only additional input needed is a single seed configuration for the system to initialize our procedure; no dataset of trajectories is required. We represent subspaces as neural networks that map a low-dimensional latent vector to the full configuration space, and propose a training scheme to fit network parameters to any system of interest. This formulation is effective across a very general range of physical systems; our experiments demonstrate not only nonlinear and very low-dimensional elastic body and cloth subspaces, but also more general systems like colliding rigid bodies and linkages. We briefly explore applications built on this formulation, including manipulation, latent interpolation, and sampling.

Nicholas Sharp, Alec Jacobson

Neural implicit representations, which encode a surface as the level set of a neural network applied to spatial coordinates, have proven to be remarkably effective for optimizing, compressing, and generating 3D geometry. Although these representations are easy to fit, it is not clear how to best evaluate geometric queries on the shape, such as intersecting against a ray or finding a closest point. The predominant approach is to encourage the network to have a signed distance property. However, this property typically holds only approximately, leading to robustness issues, and holds only at the conclusion of training, inhibiting the use of queries in loss functions. Instead, this work presents a new approach to perform queries directly on general neural implicit functions for a wide range of existing architectures. Our key tool is the application of range analysis to neural networks, using automatic arithmetic rules to bound the output of a network over a region; we conduct a study of range analysis on neural networks, and identify variants of affine arithmetic which are highly effective. We use the resulting bounds to develop geometric queries including ray casting, intersection testing, constructing spatial hierarchies, fast mesh extraction, closest-point evaluation, evaluating bulk properties, and more. Our queries can be efficiently evaluated on GPUs, and offer concrete accuracy guarantees even on randomly-initialized networks, enabling their use in training objectives and beyond. We also show a preliminary application to inverse rendering.

Nicholas Sharp, Souhaib Attaiki, Keenan Crane et al.

We introduce a new general-purpose approach to deep learning on 3D surfaces, based on the insight that a simple diffusion layer is highly effective for spatial communication. The resulting networks are automatically robust to changes in resolution and sampling of a surface -- a basic property which is crucial for practical applications. Our networks can be discretized on various geometric representations such as triangle meshes or point clouds, and can even be trained on one representation then applied to another. We optimize the spatial support of diffusion as a continuous network parameter ranging from purely local to totally global, removing the burden of manually choosing neighborhood sizes. The only other ingredients in the method are a multi-layer perceptron applied independently at each point, and spatial gradient features to support directional filters. The resulting networks are simple, robust, and efficient. Here, we focus primarily on triangle mesh surfaces, and demonstrate state-of-the-art results for a variety of tasks including surface classification, segmentation, and non-rigid correspondence.

Nicholas Sharp, Maks Ovsjanikov

This work considers a new task in geometric deep learning: generating a triangulation among a set of points in 3D space. We present PointTriNet, a differentiable and scalable approach enabling point set triangulation as a layer in 3D learning pipelines. The method iteratively applies two neural networks: a classification network predicts whether a candidate triangle should appear in the triangulation, while a proposal network suggests additional candidates. Both networks are structured as PointNets over nearby points and triangles, using a novel triangle-relative input encoding. Since these learning problems operate on local geometric data, our method is efficient and scalable, and generalizes to unseen shape categories. Our networks are trained in an unsupervised manner from a collection of shapes represented as point clouds. We demonstrate the effectiveness of this approach for classical meshing tasks, robustness to outliers, and as a component in end-to-end learning systems.