Related papers: Gaussian Mixture Flow Matching Models

Diffusion models and their variations, such as rectified flows, generate diverse and high-quality images, but they are still hindered by slow iterative sampling caused by the highly curved generative paths they learn. An important cause of…

Training deep neural networks remains computationally intensive due to the itera2 tive nature of gradient-based optimization. We propose Gradient Flow Matching (GFM), a continuous-time modeling framework that treats neural network training…

Consistency models imitate the multi-step sampling of score-based diffusion in a single forward pass of a neural network. They can be learned in two ways: consistency distillation and consistency training. The former relies on the true…

Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…

We propose a novel denoising diffusion generative model for predicting nonlinear fluid fields named FluidDiff. By performing a diffusion process, the model is able to learn a complex representation of the high-dimensional dynamic system,…

Generative models, particularly diffusion model, have emerged as powerful tools for sequential recommendation. However, accurately modeling user preferences remains challenging due to the noise perturbations inherent in the forward and…

Normalizing Flows (NFs) learn invertible mappings between the data and a Gaussian distribution. Prior works usually suffer from two limitations. First, they add random noise to training samples or VAE latents as data augmentation,…

Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but…

Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and…

In this work we tackle the problem of estimating the density $f_X$ of a random variable $X$ by successive smoothing, such that the smoothed random variable $Y$ fulfills $(\partial_t - \Delta_1)f_Y(\,\cdot\,, t) = 0$, $f_Y(\,\cdot\,, 0) =…

Diffusion models, and their generalization, flow matching, have had a remarkable impact on the field of media generation. Here, the conventional approach is to learn the complex mapping from a simple source distribution of Gaussian noise to…

Normalising flows are generative models that transform a complex density into a simpler density through the use of bijective transformations enabling both density estimation and data generation from a single model. %However, the requirement…

Iterative generative models such as Flow Matching and Diffusion models have demonstrated strong test-time scaling behavior, where additional inference computation can improve generation quality. In contrast, Drift Models offer efficient…

Existing generative models for time series forecasting often transform simple priors (typically Gaussian) into complex data distributions. However, their sampling initialization, independent of historical data, hinders the capture of…

Discrete flow models offer a powerful framework for learning distributions over discrete state spaces and have demonstrated superior performance compared to the discrete diffusion models. However, their convergence properties and error…

Deep generative models have made rapid progress in image, text, audio, and video generation, and are increasingly being applied to structured records. For tabular data, however, generative modeling remains difficult: a dataset may contain…

The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…

Most of the existing diffusion models use Gaussian noise for training and sampling across all time steps, which may not optimally account for the frequency contents reconstructed by the denoising network. Despite the diverse applications of…

We propose a principled and effective framework for one-step generative modeling. We introduce the notion of average velocity to characterize flow fields, in contrast to instantaneous velocity modeled by Flow Matching methods. A…

Low-energy molecular conformers generation (MCG) is a foundational yet challenging problem in drug discovery. Denoising-based methods include diffusion and flow-matching methods that learn mappings from a simple base distribution to the…