The theory of light transport on Gaussian process implicit surface (GPIS) provides a unified framework for rendering surfaces, participating media, and the intermediate spectrum. However, previous approaches rely on brute-force ray marching for surface intersections, requiring full noise evaluations at each marching point, whether using multivariate Gaussian sampling or sparse convolution noise approximation. This imposes a severe limitation on the rendering efficiency. In this paper, we derive bounds to significantly reduce the total number of full noise evaluations, leading to efficient ray marching for ray-surface intersections. We introduce stratified Bernoulli impulses, enabling a fast point-level bound for individual realizations to replace unnecessary full noise evaluations. To further reduce the number of point-level bound evaluations, we propose a region-level bound, leveraging a spatial acceleration structure to prune probabilistically empty regions, thereby avoiding unnecessary marching points in advance. By combining these two bounds, our bounded ray marching accelerates ray-surface intersections in GPIS, and consequently significantly improves overall GPIS rendering efficiency. Code for this paper are at https://github.com/Cchen-77/bounded-gpis.
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This paper tackles the task of learning to generate signals over triangle meshes in a triangulation-agnostic manner, meaning the trained model can be applied to different meshes and triangulations effectively. Practically, the paper adapts the flow matching (FM) paradigm to a mesh-based, triangulation-agnostic setting. Theoretically, it proposes a specific noise distribution which is triangulation agnostic, to be used inside the FM model's denoising process. While noise distributions are usually trivial to devise for, e.g., images, devising a triangulation-agnostic distribution proves to be a much more difficult task. We formulate a mathematical definition of triangulation agnosticism of distributions, via their spectrum. We then show that a discretization of a specific Gaussian random field called a Matérn process holds these desired properties, and provides a simple and efficient sampling algorithm. We use it as our noise model, and adapt FM to the triangulation-agnostic setting by using a state-of-the-art approach for learning signals on meshes in the gradient domain—PoissonNet—as the denoiser. We conduct experiments on elaborate tasks such as sampling elastic rest states, and generating poses of humanoids. Our method is shown to be capable of producing highly realistic results for meshes of over one million triangles, significantly exceeding the state-of-the-art in quality and diversity.
We present a framework for uncertainty-aware geometry processing on Gaussian Process Implicit Surfaces (GPIS), enabling computations directly on such probabilistic representations of shapes. In contrast to classical geometry processing pipelines that assume deterministic surface meshes or point clouds, our approach considers uncertainty in the input data and defines analogs of fundamental differential operators-gradient, divergence, and Laplacian- that account for the distribution of plausible geometries encoded by the GPIS. Leveraging the Kac-Rice formula, we embed computations from random surfaces into a volumetric Cartesian domain, enabling efficient evaluation of expected integrals and differential operators. The proposed approach bridges classical surface PDE-based geometry processing and volumetric representations, enabling a principled handling of noise and ambiguity for various downstream geometry processing tasks.
We propose a new framework to systematically incorporate data uncertainty in Gaussian Splatting. Being the new paradigm of neural rendering, Gaussian Splatting has been investigated in many applications, with the main effort in extending its representation, improving its optimization process, and accelerating its speed. However, one orthogonal, much needed, but under-explored area is data uncertainty. In standard 4D Gaussian Splatting, data uncertainty can manifest as view sparsity, missing frames, camera asynchronization, etc. So far, there has been little research to holistically incorporating various types of data uncertainty under a single framework. To this end, we propose Graphical X Splatting, or GraphiXS, a new probabilistic framework that considers multiple types of data uncertainty, aiming for a fundamental augmentation of the current 4D Gaussian Splatting paradigm into a probabilistic setting. GraphiXS is general and can be instantiated with a range of primitives, e.g. Gaussians, Student’s-t. Furthermore, GraphiXS can be used to ‘upgrade’ existing methods to accommodate data uncertainty. Through exhaustive evaluation and comparison, we demonstrate that GraphiXS can systematically model various uncertainties in data, outperform existing methods in many settings where data are missing or polluted in space and time, and therefore is a major generalization of the current 4D Gaussian Splatting research.
Gaussian Process Implicit Surfaces (GPIS) represent geometry as a distribution over implicit functions. Modeling an object’s appearance as the expected rendering of a GPIS yields a unified framework that captures diverse light-transport effects including microfacet-like reflections and volumetric scattering. Despite this generality, computing GPIS–ray intersections requires sampling conditional multivariate Gaussian distributions along each ray and remains prohibitively expensive. We introduce an online sampling algorithm that draws these distributions incrementally, and an adaptive marching scheme that takes large steps where the surface is provably absent, minimizing the probability of missed intersections. Together, these ideas reduce rendering MSE by up to 46 × at equal time compared to existing methods.
Surface reconstruction from unoriented point clouds is a fundamental problem in geometry processing. While recent winding-number-based approaches, such as Parametric Gauss Reconstruction (PGR) and Anisotropic Gauss Reconstruction (AGR), provide elegant implicit formulations, they often suffer from underdetermined or ill-conditioned linear systems. In this work, we analyze the theoretical root of this instability: the winding number formula is oblivious to a broad family of tangential perturbations of the normal field, which introduces a non-trivial nullspace in the resulting integral equations. To address this, we present G3R, a simple yet effective method based on Green’s third identity for harmonic functions. This approach eliminates the tangential nullspace with a basis of harmonic functions, resulting in a well-conditioned linear system which can be solved directly without additional regularization. Furthermore, we apply a Gaussian mollification of the fundamental solution, which handles near-field singularities robustly. We adopt a matrix-free implementation and accelerate it with a hierarchical scheme to scale our method to large point clouds. Experiments demonstrate that our approach achieves highly competitive performance in both normal orientation accuracy and surface reconstruction quality. Our code is publicly available at https://github.com/ne0-wu/G3R.
Text-to-image diffusion models generate images by gradually converting white Gaussian noise into a natural image. White Gaussian noise is well suited for producing diverse outputs from a single text prompt due to its absence of structure. However, this very property limits control over, and predictability of, specific visual attributes, as the noise is not human-interpretable. In this work, we investigate the characteristics of the input noise in diffusion models. We show that, although all frequencies in white Gaussian noise have comparable statistical energy, low-frequency components primarily determine the image’s global structure and color composition, while high-frequency components control finer details. Building on this observation, we demonstrate that simple manipulations of the low-frequency noise using low-frequency image priors can effectively condition the generation process to reconstruct these low-frequency visual cues. This allows us to define a simple, training-free method with minimal overhead that steers overall image structure and color, while letting high-frequency components freely emerge as fine details, enabling variability across generated outputs.
Achieving high-quality real-time rendering on mobile devices is critical for immersive 3D applications, yet 3D Gaussian Splatting (3DGS) faces significant challenges on resource-constrained mobile platforms, with sustaining 60 FPS at 2K resolution remaining difficult despite recent advances. Rather than further optimizing the core splatting pipeline, we explore 3DGS acceleration through post-rendering techniques leveraging gradient for super-sampling and frame interpolation. We propose Mobile3DGS3, a lightweight framework that alternates between super-sampling and frame interpolation. Our framework introduces three key innovations: Tangent Space Gradient Caching (TSGC), which converts gradient into cached geometric invariants enabling seamless integration with hardware-accelerated rasterization; Gradient-Aware Super-Sampling (GASS), which leverages Gaussian splat differentiability to upsample low-resolution images while preserving details; and Gradient-Aware Frame Interpolation (GAFI), which resamples gradient from adjacent frames with efficient motion vector upscaling for NPU-compatible processing. Extensive experiments demonstrate significant rendering efficiency improvements on mobile devices while maintaining high visual fidelity, presenting the first 3DGS acceleration paradigm on mobile devices that effectively leverages gradient in both super-sampling and frame interpolation. Code repository: https://github.com/SyouSanGin/Mobile3DGS3
Analysis and anomaly detection in event tensor streams consisting of timestamps and multiple attributes—such as communication logs (time, IP address, packet length)—are essential tasks in data mining. While existing tensor decomposition and anomaly detection methods provide useful insights, they face the following two limitations. (i) They cannot handle heterogeneous tensor streams, which comprises both categorical attributes (e.g., IP address) and continuous attributes (e.g., packet length). They typically require either discretizing continuous attributes or treating categorical attributes as continuous, both of which distort the underlying statistical properties of the data. Furthermore, incorrect assumptions about the distribution family of continuous attributes often degrade the model's performance. (ii) They discretize timestamps, failing to track the temporal dynamics of streams (e.g., trends, abnormal events), which makes them ineffective for detecting anomalies at the group level, referred to as ''group anomalies'' (e.g, DoS attacks). To address these challenges, we propose HeteroComp, a method for continuously summarizing heterogeneous tensor streams into ''components'' representing latent groups in each attribute and their temporal dynamics, and detecting group anomalies. Our method employs Gaussian process priors to model unknown distributions of continuous attributes, and temporal dynamics, which directly estimate probability densities from data. Extracted components give concise but effective summarization, enabling accurate group anomaly detection. Extensive experiments on real datasets demonstrate that HeteroComp outperforms the state-of-the-art algorithms for group anomaly detection accuracy, and its computational time does not depend on the data stream length.
User cold-start problem is a long-standing challenge in recommendation systems. Fortunately, cross-domain recommendation (CDR) has emerged as a highly effective remedy for the user cold-start challenge, with recently developed diffusion models (DMs) demonstrating exceptional performance. However, these DMs-based CDR methods focus on dealing with user-item interactions, overlooking correlations between items across the source and target domains. Meanwhile, the Gaussian noise added in the forward process of diffusion models would hurt user's personalized preference, leading to the difficulty in transferring user preference across domains. To this end, we propose a novel paradigm of Smoothing-Sharpening Process Model for CDR to cold-start users, termed as S2CDR which features a corruption-recovery architecture and is solved with respect to ordinary differential equations (ODEs). Specifically, the smoothing process gradually corrupts the original user-item/item-item interaction matrices derived from both domains into smoothed preference signals in a noise-free manner, and the sharpening process iteratively sharpens the preference signals to recover the unknown interactions for cold-start users. Wherein, for the smoothing process, we introduce the heat equation on the item-item similarity graph to better capture the correlations between items across domains, and further build the tailor-designed low-pass filter to filter out the high-frequency noise information for capturing user's intrinsic preference, in accordance with the graph signal processing (GSP) theory. Extensive experiments on three real-world CDR scenarios confirm that our S2CDR significantly outperforms previous SOTA methods in a training-free manner.
Forecasting state evolution of network systems, such as the spread of information on social networks, is significant for effective policy interventions and resource management. However, the underlying propagation dynamics constantly shift with new topics or events, which are modeled as changing coefficients of the underlying dynamics. Deep learning models struggle to adapt to these out-of-distribution shifts without extensive new data and retraining. To address this, we present Zero-Shot Forecasting of Network Dynamics through Weight Flow Matching (FNFM), a generative, coefficient-conditioned framework that generates dynamic model weights for an unseen target coefficient, enabling zero-shot forecasting. Our framework utilizes a Variational Encoder to summarize the forecaster weights trained in observed environments into compact latent tokens. A Conditional Flow Matching (CFM) module then learns a continuous transport from a simple Gaussian distribution to the empirical distribution of these weights, conditioned on the dynamical coefficients. This process is instantaneous at test time and requires no gradient-based optimization. Across varied dynamical coefficients, empirical results indicate that FNFM yields more reliable zero-shot accuracy than baseline methods, particularly under pronounced coefficient shift.
Graph-level anomaly detection (GLAD) is a critical task to identify graphs with abnormal properties in various domains, ranging from fraudulent social networks to malicious botnets on online platforms. The dominant paradigm for existing GLAD detectors has been partially unsupervised, relying on training data composed exclusively of normal samples. However, this partially unsupervised paradigm inevitably requires a costly expert filtering process to ensure the training data is free of anomalies. This creates a significant gap between current approaches and the real-world necessity of a fully unsupervised paradigm, which involves training a model directly on real-world data ''as-is'', with its inherent mix of normal and anomalous samples. To bridge this gap, we incorporate uncertainty learning into GLAD to promote fully unsupervised learning. We propose two frameworks: Score Uncertainty Learning (SUL) and Graph-data Uncertainty Learning (GUL). Specifically, SUL enhances existing GLAD detectors by modeling uncertainty through Gaussian distributions over the detectors' predictions, adaptively attenuating the influence of potential anomalies. GUL is an end-to-end framework that iteratively optimizes anomaly detection and uncertainty modeling via an Expectation-Maximization algorithm. In addition, we develop a dedicated loss that utilizes potential anomalies to enhance the effectiveness and robustness of GUL. Empirical results on sixteen benchmark datasets, covering real-world graphs from social networks and online platforms, demonstrate the superiority of our methods and highlight the promise of incorporating uncertainty into fully unsupervised GLAD.
Zero-shot transfer for offline reinforcement learning involves generalizing to a wide range of tasks that are often risk-sensitive, without new interaction. We show here that although Successor Features (SFs) provide a principled framework for transfer through abstracting dynamics from rewards, their typical form is restricted to expected cumulative returns and is thus indifferent to variance in returns. We contend that such a mean-centric approach introduces bias by conflating risky and safe trajectories with identical expected outcomes, as it ignores outcome dispersion critical for risk-aware evaluation. Additionally, we note that distributional methods can be employed to model outcome distributions, but frequently do so at a high computational cost due to the need for discretization or elaborate sampling. To overcome this problem, we introduce a form of successor representation that incorporates an uncertainty envelope over states: Gaussian Distributional Successor Features (GDSF). Rather than inferring an implicit generative process, GDSF learns to approximate the distribution of cumulative outcomes with a Gaussian through recursive moment-matching. We present this framework for efficient representation of aleatoric uncertainty, without resorting to computationally expensive existing distributional methods. We also introduce Latent Outcome Optimization, an inference procedure which finds high-reward outcomes in the data support and drives a goal-conditioned policy. This dual-mode design allows the agent to transfer to non-linear objectives in a zero-shot way while preserving closed-form efficiency for linear tasks. Experiments on the D4RL benchmark show that GDSF yields better performance in risk-sensitive tasks while achieving at least competitive results in standard linear regimes.
Denoising Diffusion Codebook Models (DDCM) have emerged as a promising framework for zero-shot image compression by replacing stochastic sampling with discrete selection from a reproducible Gaussian codebook. By greedily picking noise vectors that best match the target image, DDCM encodes the generative trajectory into a compact sequence of indices for image compression. However, the target-guided noise selection provides only coarse guidance as the discrepancy between the denoiser's output and the target image is substantial. This discrepancy inevitably results in trajectory drift, necessitating massive codebooks to span the enlarged search space and extensive inference steps to gradually compensate for the deviation. In this paper, we propose the Trajectory-Consistent Diffusion Codebook Model (TC-DDCM) to address these inefficiencies. Rather than approximating the distant target, TC-DDCM navigates the generative process by strictly tracking a pre-computed inversion trajectory. This paradigm shift yields two critical advantages: 1) By minimizing the deviation to the proximal reference state along the trajectory, the search space is drastically shrunk, resulting in significantly smaller codebooks. 2) By aligning the generative steps with inversion methods, TC-DDCM achieves optimal reconstruction in a few inference steps. Extensive experiments demonstrate that TC-DDCM significantly outperforms state-of-the-art zero-shot methods in rate-distortion-perception performance at ultra-low bitrates, making zero-shot diffusion-based compression practical.
The rapid advancement of generative AI has made audio deepfakes increasingly indistinguishable from authentic human vocals, posing significant threats to persons-of-interest (POI) such as public figures. Current detection systems primarily rely on generic, black-box models that fail to capture speaker-specific idiosyncratic traits and lack interpretability. In this paper, we propose Phoneme-based Voice Profiling (PVP), a novel personalized defense framework. By shifting the detection paradigm from macro-utterance analysis to micro-phonetic modeling, PVP captures the unique acoustic distributions underlying a POI’s habitual articulatory patterns. Specifically, our framework models speaker-specific phonetic realizations using lightweight Gaussian Mixture Models (GMMs) estimated solely from bona fide reference speech. This design enables data-efficient profiling and robust generalization to previously unseen spoofing attacks without requiring heavy spoof-specific training. Furthermore, we introduce the first large-scale Chinese POI deepfake dataset to benchmark speaker-specific detection. Experimental results demonstrate that PVP significantly outperforms state-of-the-art generic detectors in POI spoofing scenarios, achieving substantial EER reductions while providing fine-grained, phoneme-level interpretability for forensic analysis. Code and data are available at: https://github.com/JunXue-tech/PVP
4DVarGen: A 4D Variational-Inspired Generative Model for Eddy-Resolving Surface Ocean Reconstruction
Sea surface variable reconstruction from sparse observations is a key ocean-science challenge. Traditional methods, such as the four-dimensional variational (4DVar) approach, rely on numerical models for background information, leading to high computational costs. Deep learning methods are more efficient but often fail to capture eddy dynamics, resulting in limited effective resolution. We propose 4DVarGen, a 4DVar-inspired generative framework for reconstructing sea surface variable fields at eddy-resolving scales from sparse remote-sensing observations. 4DVarGen establishes a mathematical equivalence between 4DVar and an observation-guided denoising process. Its key innovation is injecting the observation-likelihood gradient into denoising iterations, driving the generated trajectories to evolve in the direction of minimizing the 4DVar objective function toward a maximum a posteriori solution. Spatiotemporal priors learned by a diffusion model serve as background information, reducing computational costs and mitigating the adverse effects of Gaussian assumptions. Experiments show that 4DVarGen effectively leverages the temporal evolution patterns of sea surface temperature (SST) and sea surface height (SSH), as well as their dynamical mappings learned by the diffusion model, leading to improved reconstruction accuracy and effective resolution. Our model, pretrained on GLORYS12V1 reanalysis data, generates sea surface variable fields guided by real observations, achieving accuracy and effective resolution improvements of 18% and 58%, respectively, compared to GLORYS12V1. This study offers a novel framework for reconstructing Earth system states from sparse observations.
Artificial intelligence models typically perform well on large-scale datasets, yet their effectiveness tends to degrade in real-world scenarios with scarce data, such as medical diagnostics. In contrast, humans can learn and reason effectively from few examples. Even when novel objects differ significantly from prior observations, humans can quickly infer category distributions accurately. Inspired by this, we explore how to leverage human-inspired cognitive mechanisms to improve the distribution calibration in few-shot learning models. Based on the ``fast-slow thinking'' dual-process theory, we propose a novel cognition-inspired few-shot learning framework. It mimics the human cognition when handling novel information: it first rapidly screens relevant knowledge through ``fast thinking'' and then infers inter-class relationships and calibrates distributions via ``slow thinking''. Specifically, the fast-thinking stage employs a gating mechanism to quickly match input samples with known base-class prototypes, activating relevant candidate knowledge. In the slow-thinking stage, the model aggregates inter-class edge embeddings into a summary relation graph and then applies divergent Gaussian sampling to generate multiple relation graphs representing different association strengths, thereby achieving distribution calibration for few-shot classes. Experiments on public few-shot benchmarks and medical image datasets show competitive performance. Visualization analyses further reveal that our framework exhibits meaningful interpretability.
3D Gaussian Splatting enables efficient, high-fidelity novel view synthesis with explicit Gaussians and differentiable rendering. However, adverse weather introduces rain streaks and droplets as well as volumetric scattering, producing view-dependent, spatially varying degradations that break the clean multi-view consistency assumption and lead to geometric drift and unstable appearance. Existing approaches are largely confined to the 2D image domain and seldom model the 3D degradation formation process, limiting controllable weather synthesis and consistent restoration in 3DGS. To our knowledge, we are the first to incorporate real meteorological observations as an external prior and propose a 3D-level unified rendering–restoration framework for joint deraining and dehazing within a single 3DGS pipeline. Precipitation is mapped to interpretable parameters controlling the density and morphology of rain Gaussians, while an atmospheric-scattering extinction strength drives 3D fog generation for reproducible weather modeling. We adopt a closed-loop dual-branch optimization where the rendering branch fits degraded observations to capture weather degradation patterns, and the restoration branch regularizes scene Gaussians toward a clean domain with multi-scale perceptual consistency, suppressing artifacts and improving cross-view detail fidelity. Experiments across diverse scenes and weather conditions consistently outperform strong baselines on all three metrics, with a particularly notable PSNR improvement of 1.78 dB on average.
Many real-world applications require solving families of expensive multi-objective optimization problems~(EMOPs) under varying operational conditions. This can be formulated as parametric expensive multi-objective optimization problems (P-EMOPs) where each task parameter defines a distinct optimization instance. Current multi-objective Bayesian optimization methods have been widely used for finding finite sets of Pareto optimal solutions for each task. However, P-EMOPs present a fundamental challenge: the continuous task parameter space can contain infinite distinct problems, each requiring separate expensive evaluations. To address this, we propose learning an inverse model to amortize the multi-objective optimization cost across the continuous task-preference space, enabling direct solution prediction for any query without the need for expensive re-evaluation. This paper introduces a novel parametric multi-objective Bayesian optimizer that learns this inverse model by alternating between (1) generative solution sampling via conditional generative models and (2) acquisition-driven search leveraging inter-task synergies. This approach enables effective optimization across multiple tasks and finally achieves direct solution prediction for unseen parameterized EMOPs without re-evaluations. We theoretically justify the faster convergence by leveraging inter-task synergies through task-aware Gaussian processes. Based on that, empirical studies in synthetic and real-world benchmarks further verify the effectiveness of the proposed parametric optimizer.
4D Gaussian Splatting (4DGS) enables high-quality, real-time rendering of dynamic scenes and is becoming a popular format for sharing 4D assets. This trend calls for robust copyright watermarking that can be verified from rendered videos without access to the original scene or model parameters. However, watermarking 4DGS is challenging: verification relies on short multi-view clips whose frames vary with motion, viewpoint changes, and post-processing. More importantly, decoding from rendered frames is easily dominated by scene content (objects, textures, illumination) rather than subtle watermark traces, leading to unstable evidence across frames and poor generalization across scenes. We propose Guard4D, a decoupled watermarking framework for 4DGS. Guard4D pre-trains a general-purpose message decoder under text supervision and embeds a binary message by optimizing compact spherical-harmonic offsets while keeping geometry and opacity fixed. To improve extraction from short clips and suppress semantic interference, we introduce a temporal modeling and semantic decoupling (TMSD) module that temporally aggregates watermark information and uses clean and noise-perturbed control clips generated from the non-watermarked model to reduce the influence of semantics on watermark decoding. Extensive experiments on dynamic 4DGS scenes demonstrate the effectiveness of Guard4D. Code is available at https://github.com/shisyy/Guard4D.