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Mesh is a fundamental representation of 3D assets in various industrial applications, and is widely supported by professional softwares. However, due to its irregular structure, mesh creation and manipulation is often time-consuming and labor-intensive. In this paper, we propose a highly controllable generative model, GetMesh, for mesh generation and manipulation across different categories. By taking a varying number of points as the latent representation, and re-organizing them as triplane representation, GetMesh generates meshes with rich and sharp details, outperforming both single-category and multi-category counterparts. Moreover, it also enables fine-grained control over the generation process that previous mesh generative models cannot achieve, where changing global/local mesh topologies, adding/removing mesh parts, and combining mesh parts across categories can be intuitively, efficiently, and robustly accomplished by adjusting the number, positions or features of latent points. Project page is https://getmesh.github.io.

Mesh generation is of great value in various applications involving computer graphics and virtual content, yet designing generative models for meshes is challenging due to their irregular data structure and inconsistent topology of meshes in the same category. In this work, we design a novel sparse latent point diffusion model for mesh generation. Our key insight is to regard point clouds as an intermediate representation of meshes, and model the distribution of point clouds instead. While meshes can be generated from point clouds via techniques like Shape as Points (SAP), the challenges of directly generating meshes can be effectively avoided. To boost the efficiency and controllability of our mesh generation method, we propose to further encode point clouds to a set of sparse latent points with point-wise semantic meaningful features, where two DDPMs are trained in the space of sparse latent points to respectively model the distribution of the latent point positions and features at these latent points. We find that sampling in this latent space is faster than directly sampling dense point clouds. Moreover, the sparse latent points also enable us to explicitly control both the overall structures and local details of the generated meshes. Extensive experiments are conducted on the ShapeNet dataset, where our proposed sparse latent point diffusion model achieves superior performance in terms of generation quality and controllability when compared to existing methods., Comment: Accepted to CVPR 2023. Project page is at https://slide-3d.github.io

With wider application of deep neural networks (DNNs) in various algorithms and frameworks, security threats have become one of the concerns. Adversarial attacks disturb DNN-based image classifiers, in which attackers can intentionally add imperceptible adversarial perturbations on input images to fool the classifiers. In this paper, we propose a novel purification approach, referred to as guided diffusion model for purification (GDMP), to help protect classifiers from adversarial attacks. The core of our approach is to embed purification into the diffusion denoising process of a Denoised Diffusion Probabilistic Model (DDPM), so that its diffusion process could submerge the adversarial perturbations with gradually added Gaussian noises, and both of these noises can be simultaneously removed following a guided denoising process. On our comprehensive experiments across various datasets, the proposed GDMP is shown to reduce the perturbations raised by adversarial attacks to a shallow range, thereby significantly improving the correctness of classification. GDMP improves the robust accuracy by 5%, obtaining 90.1% under PGD attack on the CIFAR10 dataset. Moreover, GDMP achieves 70.94% robustness on the challenging ImageNet dataset.

In this work, we consider the fundamental problem of deriving quantitative bounds on the probability that a given assertion is violated in a probabilistic program. We provide automated algorithms that obtain both lower and upper bounds on the assertion violation probability in exponential forms. The main novelty of our approach is that we prove new and dedicated fixed-point theorems which serve as the theoretical basis of our algorithms and enable us to reason about assertion violation bounds in terms of pre and post fixed-point functions. To synthesize such fixed-points, we devise algorithms that utilize a wide range of mathematical tools, including repulsing ranking super-martingales, Hoeffding's lemma, Minkowski decompositions, Jensen's inequality, and convex optimization. On the theoretical side, we provide (i) the first automated algorithm for lower-bounds on assertion violation probabilities, (ii) the first complete algorithm for upper-bounds of exponential form in affine programs, and (iii) provably and significantly tighter upper-bounds than the previous approach of stochastic invariants. On the practical side, we show that our algorithms can handle a wide variety of programs from the literature and synthesize bounds that are several orders of magnitude tighter in comparison with previous approaches., Comment: 25 pages

Analyzing probabilistic programs and randomized algorithms are classical problems in computer science. The first basic problem in the analysis of stochastic processes is to consider the expectation or mean, and another basic problem is to consider concentration bounds, i.e. showing that large deviations from the mean have small probability. Similarly, in the context of probabilistic programs and randomized algorithms, the analysis of expected termination time/running time and their concentration bounds are fundamental problems.In this work, we focus on concentration bounds for probabilistic programs and probabilistic recurrences of randomized algorithms. For probabilistic programs, the basic technique to achieve concentration bounds is to consider martingales and apply the classical Azuma's inequality. For probabilistic recurrences of randomized algorithms, Karp's classical "cookbook" method, which is similar to the master theorem for recurrences, is the standard approach to obtain concentration bounds. In this work, we propose a novel approach for deriving concentration bounds for probabilistic programs and probabilistic recurrence relations through the synthesis of exponential supermartingales. For probabilistic programs, we present algorithms for synthesis of such supermartingales in several cases. We also show that our approach can derive better concentration bounds than simply applying the classical Azuma's inequality over various probabilistic programs considered in the literature. For probabilistic recurrences, our approach can derive tighter bounds than the Karp's well-established methods on classical algorithms. Moreover, we show that our approach could derive bounds comparable to the optimal bound for quicksort, proposed by McDiarmid and Hayward. We also present a prototype implementation that can automatically infer these bounds, Comment: 28 pages