We introduce Soft Anisotropic Diagrams (SAD), an explicit and differentiable image representation parameterized by a set of adaptive sites in the image plane. In SAD, each site specifies an anisotropic metric and an additively weighted distance score, and we compute pixel colors as a softmax blend over a small per-pixel top-K subset of sites. We induce a soft anisotropic additively weighted Voronoi partition (i.e., an Apollonius diagram) with learnable persite temperatures, preserving informative gradients while allowing clear, content-aligned boundaries and explicit ownership. Such a formulation enables efficient rendering by maintaining a per-query top-K map that approximates nearest neighbors under the same shading score, allowing GPU-friendly, fixed-size local computation. We update this list using our top-K propagation scheme inspired by jump flooding, augmented with stochastic injection to provide probabilistic global coverage. Training follows a GPU-first pipeline with gradient-weighted initialization, Adam optimization, and adaptive budget control through densification and pruning. Across standard benchmarks, SAD consistently outperforms Image-GS and Instant-NGP at matched bitrate. On Kodak, SAD reaches 46.0 dB PSNR with 2.2 s encoding time (vs. 28s for Image-GS), and delivers 4–19× end-to-end training speedups over state-of-the-art baselines. We demonstrate the effectiveness of SAD by showcasing the seamless integration with differentiable pipelines for forward and inverse problems, efficiency of fast random access, and compact storage. You can find the code here: https://luckyiyi.github.io/SAD.
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Many non-photorealistic rendering (NPR) styles, such as feature lines and hatching, are defined by image-space structure inherited from hand-drawn media. While recent path-space formulations like the stylized rendering equation (SRE) enable stylization to interact naturally with light transport, they provide no mechanism for enforcing image-space consistency. We present a conceptual framework for lifting image-space stylizations into path-space in a principled, SRE-compatible manner. Our key observation is that image-space consistency can be achieved by establishing geometrically-driven mappings from image-space to path-space. We demonstrate this through two complementary stylizations: feature lines and tone. For feature line rendering, we introduce a conditional lifting based on partial path-space variation, where a geometric path parametrization is combined with parallel transport to preserve image-space structure under distribution effects. This enables a curvature-aware, stochastic, geometry-driven formulation of line detection that generalizes prior ray-based methods. For tone-based styles, such as hatching and halftone, we propose a canonical lifting anchored to a material-independent mapping, motivated by stationary-phase arguments from wave optics. Its locally invertible approximation enables evaluation of image-space tone fields at arbitrary path vertices while preserving image-space structure under complex light transport. Both methods are implemented as ordinary style functions under the SRE and work with existing estimation and sampling strategies; demonstrating how image-space structure can be preserved within path-space rendering, enabling a broader class of expressive, physically-grounded NPR styles.
Elliptic partial differential equations are ubiquitous in graphics and engineering, but remain challenging to solve on complex or evolving geometries. Traditional discretization schemes (e.g., FEM/FDM) provide stable, globally coupled solutions but require heavy meshing or extreme refinement to accurately resolve geometric detail. In contrast, grid-free Monte Carlo methods (e.g., Walk on Spheres/Stars) adapt naturally to arbitrary geometry and offer massive parallelism, but rely on long random walks whose variance grows rapidly, particularly in the presence of Neumann boundaries, leading to slow convergence. We introduce a hybrid approach that combines the geometric flexibility of Monte Carlo estimation with deterministic global solves that do not introduce additional stochastic error. Our method decomposes the domain into simple, regular subdomains and uses Monte Carlo to estimate local first-passage solution operators (Poisson kernels), where walk lengths and variance are inherently controlled by the reduced spatial scale. These local operators are assembled into a sparse global system whose solution is obtained via a deterministic linear solve that exactly replaces simulating discrete random walks throughout the domain. This global solve trades stochastic variance for a fixed, resolution-dependent discretization bias, yielding stable and reusable solution operators. As a result, our method attains accurate, geometry-aware solutions even on coarse discretizations, and enables efficient solves and re-solves by computing and updating only the local operators affected by the geometry and its changes. We evaluate the approach on complex two-dimensional domains, benchmarking accuracy and convergence against standard grid-free and grid-based baselines, and demonstrate applications to microstructure simulation and flow-based path planning and streamline visualization.
Stochastic Monte Carlo solvers for partial differential equations (PDEs) recently gained popularity in computer graphics, finding applications in geometry processing, rendering, simulation, and visualization. At present, there exists no Monte Carlo solver for the rendering of biharmonic diffusion curves, an artist-friendly smooth vector graphics primitive. The fourth-order biharmonic equation of biharmonic diffusion curves can be split into two second-order PDEs, namely a Laplace and a Poisson equation. However, since biharmonic diffusion curves set Dirichlet and inhomogeneous Neumann conditions at the same time, these two second-order PDEs are tightly coupled and can hence not be solved directly. We propose to treat the rendering of biharmonic diffusion curves as an inverse problem, in which the Dirichlet data of the Laplace equation is unknown. We formulate a variational energy optimization, such that the user-defined boundary conditions are met. Thereby, the necessary gradients are estimated stochastically by solving two second-order problems with Dirichlet boundary conditions only.
In this paper, we study an under-explored but important factor of diffusion generative models, i.e., the combinatorial complexity. Data samples are generally high-dimensional, and for various structured generation tasks, additional attributes are combined to associate with data samples. We show that the space spanned by the combination of dimensions and attributes can be insufficiently covered by existing training schemes of diffusion generative models, potentially limiting test time performance. We present a simple fix to this problem by constructing stochastic processes that fully exploit the combinatorial structures, hence the name ComboStoc. Using this simple strategy, we show that network training is significantly accelerated across diverse data modalities, including images and 3D structured shapes. Moreover, ComboStoc enables a new way of test time generation which uses asynchronous time steps for different dimensions and attributes, thus allowing for varying degrees of control over them. Our code is available at: https://github.com/Xrvitd/ComboStoc.
In this paper, we propose an efficient method for hair and fur rendering that approximates multiple scattering as volumetric light transport, achieving near path-traced visual fidelity at a drastically reduced cost. Multiple scattering among hair fibers is crucial for a realistic appearance, especially for light-colored hair, but it is extremely expensive to simulate directly. Prior approximations, such as dual scattering and fur BSSRDF, improve performance but often fail for dense hair/fur, yielding an overly dry or blurred appearance. Unlike previous volumetric hair rendering solutions, we treat dense hair/fur as a highly anisotropic participating medium to capture soft volumetric illumination, while still using explicit fiber geometry for direct lighting to preserve fine details. We accumulate hair fiber coverage in screen space and stochastically sample a single-scattering event to approximate higher-order scattering. Our method reproduces the rich appearance of hair and fur resulting from multiple scattering, while running about 7–10× faster than path tracing, making it suitable for use in production. We also demonstrate that our approach is robust under a variety of lighting conditions.
Real-time path tracing increasingly operates under extremely low sampling budgets, often below one sample per pixel, as rendering complexity, resolution, and frame-rate requirements continue to rise. Superresolution is widely used in production because it reduces path-tracing cost by tracing rays on a coarser image grid and reconstructing missing details. This creates a uniform tradeoff between cost and spatial detail: every image region receives the same reduced ray budget, although path-tracing noise, reconstruction difficulty, and perceptual importance vary strongly across the image. Adaptive sampling offers a compelling alternative, but existing end-to-end approaches rely on approximations that break down in sparse regimes. We introduce an end-to-end adaptive sampling and denoising pipeline explicitly designed for the sub-1-spp regime. Our method uses a stochastic formulation of sample placement that enables gradient estimation despite discrete sampling decisions, allowing stable training of a neural sampler at low sampling budgets. To better align optimization with human perception, we propose a tone-mapping-aware training pipeline that integrates differentiable filmic operators and a state-of-the-art perceptual loss, preventing oversampling of regions with low visual impact. In addition, we introduce a gather-based pyramidal denoising filter and a learnable generalization of albedo demodulation tailored to sparse sampling. Our results show consistent improvements over uniform sparse sampling, with notably better reconstruction of perceptually critical details such as specular highlights and shadow boundaries, and demonstrate that adaptive sampling remains effective in the sub-1-spp regime.
Mountainous terrains evolve over geological timescales through erosion processes driven by the complex interplay of transported quantities such as water, sediment, and rockfall. A key challenge in erosion modeling is the simultaneous simulation of transport and erosive processes, which differ in temporal scales by several orders of magnitude. We address this challenge with a novel, parallel, stochastic particle-based method capable of simulating transport over geological timescales. Our approach relaxes the strong assumptions on velocity required by prior works (e.g., based on the Stream Power Law), enabling a new erosion model grounded in a more general form of momentum conservation. We demonstrate that our scheme accurately solves the underlying conservation laws and avoids artifacts common in previous works. Furthermore, we show that our new erosion model captures multiscale geomorphological features, producing coherent basin structures and dynamic phenomena such as braided rivers, meanders, and deltas.
Gaussian-based representations have enabled efficient physically-based volume rendering at a fraction of the memory cost of regular, discrete, voxel-based distributions. One of the remaining advantages of classic voxel grids, however, is the ease of constructing hierarchical representations by either storing volumetric mipmaps or selectively pruning branches of an already hierarchical voxel grid. Such strategies reduce rendering time and eliminate aliasing when lower levels of detail are required. Constructing similar strategies for Gaussian-based volumes is not trivial. Straightforward solutions, such as prefiltering or computing mipmap-style representations, lead to increased memory requirements or expensive re-fitting of each level separately. Additionally, such solutions do not guarantee a smooth transition between different hierarchy levels. To address these limitations, we propose Gabor Fields, a mixture of Gabor kernels that enables continuous, orientation-selective frequency filtering at no cost. The frequency content of the asset is reduced by selectively pruning primitives, directly benefiting rendering performance, without refitting or extra storage. Beyond filtering, we demonstrate that stochastically sampling from different frequencies and orientations at each ray recursion enables masking substantial portions of the volume, accelerating ray traversal time in single- and multiple-scattering settings. Furthermore, inspired by procedural volumes, we present an application for efficient design and rendering of procedural clouds as Gabor-noise-modulated Gaussians.
Recent progress has shown that video diffusion models (VDMs) can be repurposed to solve various multimodal graphics tasks. However, existing approaches predominantly train separate models for each specific problem setting. This practice locks models into fixed input-output mappings, and typically ignores the joint correlations across modalities. In this paper, we present UniVidX, a unified multimodal framework designed to leverage VDM priors to enable versatile video generation. Our goal is to (i) master diverse pixel-aligned tasks by formulating them as conditional generation problems within multimodal space, (ii) adapt to modality-specific distributions without compromising the backbone's native priors, and (iii) ensure cross-modal consistency during synthesis. Concretely, we propose three key designs: 1) Stochastic Condition Masking (SCM): by randomly partitioning modalities into clean conditions and noisy targets during training, we enable the model to learn omni-directional conditional generation rather than fixed mappings. 2) Decoupled Gated LoRA (DGL): we attach per-modality LoRAs and activate them when a modality serves as a generation target, thereby preserving the VDM's strong priors. 3) Cross-Modal Self-Attention (CMSA): we explicitly share keys/values across modalities while maintaining modality-specific queries, facilitating information exchange and inter-modal alignment. We validate our framework by instantiating it in two domains: 1) UniVid-Intrinsic for RGB videos and their intrinsic maps (albedo, irradiance, normal), and 2) UniVid-Alpha for blended RGB videos and their constituent RGBA layers. Experimental results demonstrate that both models achieve performance competitive with state-of-the-art methods across distinct tasks. Notably, they exhibit robust generalization capabilities in in-the-wild scenarios, even when trained on limited datasets of fewer than 1k videos.
We propose Gaussian point splatting, a stochastic method to render Gaussian splats that scales extremely well to scenes with many Gaussians. Our core idea is to sample pixel-sized, opaque points from the Gaussians and to splat them to a framebuffer using 64–bit atomics. Through parallel programming primitives, we achieve an even distribution of the workload across millions of threads. Since these threads splat points independently, multiple points may splat to the same pixel. That makes it non-trivial to determine how many points should be splatted for a Gaussian or how they should be distributed to achieve the desired opacity. We successfully formalize and solve these problems, thus keeping our renders faithful to the original Gaussian splatting. To further accelerate our method, we employ hierarchical frustum and occlusion culling. Our method renders hundreds of millions of Gaussians in real time. The only differences compared to the original Gaussian splatting are slight noise and differences in aliasing.
Adaptive densification is the engine of 3D Gaussian Splatting (3DGS). However, when transposed to the optimization-based Generative Distillation paradigm, this reconstruction-native mechanism reveals fundamental limitations, resulting in inefficient representations cluttered with redundant primitives. We diagnose this failure as a Densification Dilemma stemming from the stochastic nature of generative guidance: the standard magnitude-based accumulation indiscriminately aggregates transient noise alongside geometric signals, making it difficult to strike a balance between over-densification and under-fitting. To resolve this, we introduce Context-Adaptive Moment Estimation (CAdam), a novel framework that reinterprets densification as a statistically grounded signal verification problem. CAdam leverages the first moment of gradients to exploit the interference principle—where stochastic fluctuations cancel out via destructive interference while consistent geometric drifts accumulate via constructive interference—effectively disentangling the underlying signal from the generative noise floor. This is further augmented by a quantile-based context awareness and an intrinsic Signal-to-Noise Ratio (SNR) gating mechanism, which ensure robust adaptation across optimization stages and enable the soft termination of densification. Extensive experiments across diverse objectives (SDS, ISM, VFDS) and strong generative 3DGS backbones show that CAdam reduces Gaussian count by 85%–97% relative to standard densification while preserving overall comparable perceptual quality. These results highlight signal-aware density control as a practical way to improve memory efficiency in optimization-based generative distillation.
This paper presents a modern, comprehensive system for real-time light field path tracing, addressing the prohibitive computational overhead inherent in driving high-density 3D displays. While offering immersive glasses-free 3D experiences, these displays necessitate the synthesis of massive angular information across numerous viewpoints to satisfy their optical requirements. Conventional rendering pipelines often overlook the hardware’s intrinsic spatial-angular mapping, resulting in redundant computations and extreme ray counts that preclude interactive performance. We resolve this by reformulating light field synthesis as a sparse signal reconstruction task on a high-dimensional manifold. We introduce a unified algebraic framework governed by three mathematical primitives that respectively decouple rendering logic from heterogeneous optical hardware, establish deterministic geometric connectivity across disparate viewpoints, and enable atomic access to unstructured sparse data. Leveraging this formalism, we propose a geometry-driven active sensing pipeline. By modulating a stochastic checkerboard sampling pattern with local disparity cues and coupling this with 5D temporal accumulation and unified spatio-angular integration, our method proactively allocates ray budgets to geometrically complex regions. We demonstrate a complete end-to-end system capable of driving 8K light field displays at interactive frame rates using a single consumer GPU. Our approach not only significantly outperforms existing baselines in computational efficiency and reconstruction fidelity but also naturally supports complex modern light transport effects. Project Page: https://coronaengine.github.io/ssat-page
Large language models (LLMs) are increasingly deployed in domains where errors carry high social, scientific, or safety costs. Yet standard confidence estimators, such as token likelihood, semantic similarity and multi-sample consistency, remain brittle under distribution shift, domain-specialised text, and compute limits. In this work, we present Structural Confidence, a single-pass, model-agnostic framework that enhances output correctness prediction based on multi-scale structural signals derived from a model's final-layer hidden-state trajectory. By combining spectral, local-variation, and global shape descriptors, our method captures internal stability patterns that are missed by probabilities and sentence embeddings. We conduct extensive, cross-domain evaluation across four heterogeneous benchmarks—FEVER (fact verification), SciFact (scientific claims), WikiBio-hallucination (biographical consistency), and TruthfulQA (truthfulness-oriented QA). Our Structural Confidence framework demonstrates strong performance compared with established baselines in terms of AUROC and AUPR. More importantly, unlike sampling-based consistency methods which require multiple stochastic generations and an auxiliary model, our approach uses a single deterministic forward pass, offering a practical basis for efficient, robust post-hoc confidence estimation in socially impactful, resource-constrained LLM applications.
We present BanditLP, a scalable multi-stakeholder contextual bandit framework that unifies neural Thompson Sampling (TS) for learning objective-specific outcomes with a large-scale linear program (LP) for constrained action selection at serving time. The methodology is application-agnostic, compatible with arbitrary neural architectures, and deployable at web scale, with an LP solver capable of handling billions of variables. Experiments on public benchmarks and synthetic data show consistent gains over strong baselines. We apply this approach in LinkedIn's email marketing system and demonstrate business win, illustrating the value of integrated exploration and constrained optimization in production.
User interest is not static but rather a continuously evolving process shaped by diverse interactions across multimodal web platforms. Traditional recommendation systems often model user preferences as discrete snapshots or oversimplified trajectories, failing to capture the nuanced dynamics of interest evolution. In this work, we propose Drifting with Intent, a novel framework that formalizes user interest as a continuous-time stochastic process governed by spatio-temporal coupled stochastic differential equations (SDEs). Our approach fundamentally departs from diffusion-based methods by modeling interest evolution as a directed drift toward meaningful content rather than random diffusion. The core innovation lies in a multi-granularity hypergraph encoder that captures cross-scale user-item interactions, coupled with a unified SDE solver that generates personalized interest trajectories across temporal and relational dimensions. Unlike prior work employing redundant twin networks, we introduce a generative-discriminative co-optimization framework that efficiently balances content generation and recommendation precision within a single parameter space. Extensive experiments across eight diverse datasets demonstrate that our framework not only outperforms state-of-the-art methods in recommendation quality but also provides interpretable interest trajectories that reveal how user preferences evolve across different modalities and time scales. Our work bridges the gap between generative modeling and practical recommendation systems by treating user interest as a purposeful drift rather than a random walk.
The rise of Internet of Vehicles (IoV) technologies is transforming traffic management from isolated control to a collective, multi-vehicle process. At the heart of this shift is multi-vehicle dynamic navigation, which requires simultaneously routing large fleets under evolving traffic conditions. Existing path search algorithms and reinforcement learning methods struggle to scale to city-wide networks, often failing to capture the nonlinear, stochastic, and coupled dynamics of urban traffic. To address these challenges, we propose CityNav, a hierarchical, LLM-powered framework for large-scale multi-vehicle navigation. CityNav integrates a global traffic allocation agent, which coordinates strategic traffic flow distribution across regions, with local navigation agents that generate locally adaptive routes aligned with global directives. To enable effective cooperation, we introduce a cooperative reasoning optimization mechanism, in which agents are jointly trained with a dual-reward structure: individual rewards promote per-vehicle efficiency, while shared rewards encourage network-wide coordination and congestion reduction. Extensive experiments on four real-world road networks of varying scales (up to 1.6 million roads and 430,000 intersections) and traffic datasets demonstrate that CityNav consistently outperforms nine classical path search and RL-based baselines in city-scale travel efficiency and congestion mitigation. Our results highlight the potential of LLMs to enable scalable, adaptive, and cooperative city-wide traffic navigation, providing a foundation for intelligent, large-scale vehicle routing in complex urban environments. Our project is available at https://github.com/usail-hkust/CityNav.
Link prediction is a cornerstone of the Web ecosystem, powering applications from recommendation and search to knowledge graph completion and collaboration forecasting. However, large-scale networks present unique challenges: they contain hundreds of thousands of nodes and edges with heterogeneous and overlapping community structures that evolve over time. Existing approaches face notable limitations: traditional graph neural networks struggle to capture global structural dependencies, while recent graph transformers achieve strong performance but incur quadratic complexity and lack interpretable latent structure. We propose TGSBM (Transformer-Guided Stochastic Block Model), a framework that integrates the principled generative structure of Overlapping Stochastic Block Models with the representational power of sparse Graph Transformers. TGSBM comprises three main components: (i) expander-augmented sparse attention that enables near-linear complexity and efficient global mixing, (ii) a neural variational encoder that infers structured posteriors over community memberships and strengths, and (iii) a neural edge decoder that reconstructs links via OSBM's generative process, preserving interpretability. Experiments across diverse benchmarks demonstrate competitive performance (mean rank 1.6 under HeaRT protocol), superior scalability (up to 6× faster training), and interpretable community structures. These results position TGSBM as a practical approach that strikes a balance between accuracy, efficiency, and transparency for large-scale link prediction.
Digital labor markets are increasingly used to procure diverse forms of human input, from data annotation to food delivery. A central concern in such markets is the ability of platforms to suppress wages by exploiting the abundance of low-cost labor. To better understand labor outcomes, we introduce a novel posted-price procurement model with coverage objectives. In our model a platform seeks to acquire a set of M tasks while minimizing wait time, as well as total spending. Workers are sampled from a population and complete a task if the posted price is higher than their estimated cost of labor. First, we show that with a simple pricing strategy the platform can cover all categories in time O(M), while paying only a O(log(M)/M) fraction of the total cost of labor by exploiting high worker uncertainty about their costs. Then, we study the impact of collective action to prevent the exploitation of workers. We show how a small, strategically chosen coalition of workers that commits to a price floor forces the platform's total spending from logarithmic to linear in M, substantially reducing the power of the platform to suppress wages. In contrast, a randomly sampled coalition of equal size remains largely ineffective. We complement our theory with synthetic experiments that demonstrate the benefit of targeted recruitment for collective action across different market regimes. More broadly, our results provide a theoretical foundation for understanding how to organize collective bargaining for promoting welfare in digital labor markets.