- Riemannian Diffusion Models(arXiv)
Abstract : Diffusion models are recent state-of-the-art methods for image generation and likelihood estimation. In this work, we generalize continuous-time diffusion models to arbitrary Riemannian manifolds and derive a variational framework for likelihood estimation. Computationally, we propose new methods for computing the Riemannian divergence which is needed in the likelihood estimation. Moreover, in generalizing the Euclidean case, we prove that maximizing this variational lower-bound is equivalent to Riemannian score matching. Empirically, we demonstrate the expressive power of Riemannian diffusion models on a wide spectrum of smooth manifolds, such as spheres, tori, hyperboloids, and orthogonal groups. Our proposed method achieves new state-of-the-art likelihoods on all benchmarks
2. Estimation and Specification Test for Diffusion Models with Stochastic Volatility(arXiv)
Abstract : Given the importance of continuous-time stochastic volatility models to describe the dynamics of interest rates, we propose a goodness-of-fit test for the parametric form of the drift and diffusion functions, based on a marked empirical process of the residuals. The test statistics are constructed using a continuous functional (Kolmogorov-Smirnov and Cramér-von Mises) over the empirical processes. In order to evaluate the proposed tests, we implement a simulation study, where a bootstrap method is considered for the calibration of the tests. As the estimation of diffusion models with stochastic volatility based on discretely sampled data has proven difficult, we address this issue by means of a Monte Carlo study for different estimation procedures. Finally, an application of the procedures to real data is provided.
3.Vector Quantized Diffusion Model with CodeUnet for Text-to-Sign Pose Sequences Generation (arXiv)
Abstract : Sign Language Production (SLP) aims to translate spoken languages into sign sequences automatically. The core process of SLP is to transform sign gloss sequences into their corresponding sign pose sequences (G2P). Most existing G2P models usually perform this conditional long-range generation in an autoregressive manner, which inevitably leads to an accumulation of errors. To address this issue, we propose a vector quantized diffusion method for conditional pose sequences generation, called PoseVQ-Diffusion, which is an iterative non-autoregressive method. Specifically, we first introduce a vector quantized variational autoencoder (Pose-VQVAE) model to represent a pose sequence as a sequence of latent codes. Then we model the latent discrete space by an extension of the recently developed diffusion architecture. To better leverage the spatial-temporal information, we introduce a novel architecture, namely CodeUnet, to generate higher quality pose sequence in the discrete space. Moreover, taking advantage of the learned codes, we develop a novel sequential k-nearest-neighbours method to predict the variable lengths of pose sequences for corresponding gloss sequences. Consequently, compared with the autoregressive G2P models, our model has a faster sampling speed and produces significantly better results. Compared with previous non-autoregressive G2P methods, PoseVQ-Diffusion improves the predicted results with iterative refinements, thus achieving state-of-the-art results on the SLP evaluation benchmark.
4. TopoDiff: A Performance and Constraint-Guided Diffusion Model for Topology Optimization(arXiv)
Abstract : Structural topology optimization, which aims to find the optimal physical structure that maximizes mechanical performance, is vital in engineering design applications in aerospace, mechanical, and civil engineering. Generative adversarial networks (GANs) have recently emerged as a popular alternative to traditional iterative topology optimization methods. However, these models are often difficult to train, have limited generalizability, and due to their goal of mimicking optimal topologies, neglect manufacturability and performance objectives like mechanical compliance. We propose TopoDiff, a conditional diffusion-model-based architecture to perform performance-aware and manufacturability-aware topology optimization that overcomes these issues. Our model introduces a surrogate model-based guidance strategy that actively favors structures with low compliance and good manufacturability. Our method significantly outperforms a state-of-art conditional GAN by reducing the average error on physical performance by a factor of eight and by producing 11 times fewer infeasible samples. By introducing diffusion models to topology optimization, we show that conditional diffusion models have the ability to outperform GANs in engineering design synthesis applications too. Our work also suggests a general framework for engineering optimization problems using diffusion models and external performance and constraint-aware guidance