Related papers: Incremental Generation is Necessary and Sufficient…

We provide attainable analytical tools to estimate the error of flow-based generative models under the Wasserstein metric and to establish the optimal sampling iteration complexity bound with respect to dimension as $O(\sqrt{d})$. We show…

In this work, we propose a new family of generative flows on an augmented data space, with an aim to improve expressivity without drastically increasing the computational cost of sampling and evaluation of a lower bound on the likelihood.…

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only…

Recent studies suggest utilizing generative models instead of traditional auto-regressive algorithms for time series forecasting (TSF) tasks. These non-auto-regressive approaches involving different generative methods, including GAN,…

Normalizing flows are a class of flexible deep generative models that offer easy likelihood computation. Despite their empirical success, there is little theoretical understanding of their expressiveness. In this work, we study residual…

Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…

Flow Matching, a promising approach in generative modeling, has recently gained popularity. Relying on ordinary differential equations, it offers a simple and flexible alternative to diffusion models, which are currently the…

Stability and robustness are critical for deploying Transformers in safety-sensitive settings. A principled way to enforce such behavior is to constrain the model's Lipschitz constant. However, approximation-theoretic guarantees for…

We show that the standard discrete update rule of transformer layers can be naturally interpreted as a forward Euler discretization of a continuous dynamical system. Our Transformer Flow Approximation Theorem demonstrates that, under…

Many generative models originally developed in finite-dimensional Euclidean space have functional generalizations in infinite-dimensional settings. However, the extension of rectified flow to infinite-dimensional spaces remains unexplored.…

Normalizing flows have grown more popular over the last few years; however, they continue to be computationally expensive, making them difficult to be accepted into the broader machine learning community. In this paper, we introduce a…

Normalizing Flows are generative models that directly maximize the likelihood. Previously, the design of normalizing flows was largely constrained by the need for analytical invertibility. We overcome this constraint by a training procedure…

1-Lipschitz neural networks are fundamental for generative modelling, inverse problems, and robust classifiers. In this paper, we focus on 1-Lipschitz residual networks (ResNets) based on explicit Euler steps of negative gradient flows and…

Denoising-based models, including diffusion and flow matching, have led to substantial advances in graph generation. Despite this progress, such models remain constrained by two fundamental limitations: a computational cost that scales…

Flow-based generative models are powerful exact likelihood models with efficient sampling and inference. Despite their computational efficiency, flow-based models generally have much worse density modeling performance compared to…

Generative neural networks have been empirically found very promising in providing effective structural priors for compressed sensing, since they can be trained to span low-dimensional data manifolds in high-dimensional signal spaces.…

We present theoretical convergence guarantees for ODE-based generative models, specifically flow matching. We use a pre-trained autoencoder network to map high-dimensional original inputs to a low-dimensional latent space, where a…

Denoising generative models, such as diffusion and flow-based models, produce high-quality samples but require many denoising steps due to discretization error. Flow maps, which estimate the average velocity between timesteps, mitigate this…

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied…

Gaussian denoising has emerged as a powerful method for constructing simulation-free continuous normalizing flows for generative modeling. Despite their empirical successes, theoretical properties of these flows and the regularizing effect…