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We study the problem of training a flow-based generative model, parametrized by a two-layer autoencoder, to sample from a high-dimensional Gaussian mixture. We provide a sharp end-to-end analysis of the problem. First, we provide a tight…

In this manuscript, we consider the problem of learning a flow or diffusion-based generative model parametrized by a two-layer auto-encoder, trained with online stochastic gradient descent, on a high-dimensional target density with an…

Gradient-based learning in multi-layer neural networks displays a number of striking features. In particular, the decrease rate of empirical risk is non-monotone even after averaging over large batches. Long plateaus in which one observes…

Popular generative model learning methods such as Generative Adversarial Networks (GANs), and Variational Autoencoders (VAE) enforce the latent representation to follow simple distributions such as isotropic Gaussian. In this paper, we…

Multi-modal data-sets are ubiquitous in modern applications, and multi-modal Variational Autoencoders are a popular family of models that aim to learn a joint representation of the different modalities. However, existing approaches suffer…

Phase segregation, the process by which the components of a binary mixture spontaneously separate, is a key process in the evolution and design of many chemical, mechanical, and biological systems. In this work, we present a data-driven…

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…

Flow-based models have proven successful for time-series generation, particularly when defined in lower-dimensional latent spaces that enable efficient sampling. However, how to design latent representations with desirable equivariance…

The present work proposes an inflow turbulence generation strategy using deep learning methods. This is achieved with the help of an autoencoder architecture with two different types of operational layers in the latent-space: a fully…

Current state-of-the-art generative approaches frequently rely on a two-stage training procedure, where an autoencoder (often a VAE) first performs dimensionality reduction, followed by training a generative model on the learned latent…

Continuously-observed event occurrences, often exhibit self- and mutually-exciting effects, which can be well modeled using temporal point processes. Beyond that, these event dynamics may also change over time, with certain periodic trends.…

In this work, we propose the Generative Latent Flow (GLF), an algorithm for generative modeling of the data distribution. GLF uses an Auto-encoder (AE) to learn latent representations of the data, and a normalizing flow to map the…

Test-time training adapts to a new test distribution on the fly by optimizing a model for each test input using self-supervision. In this paper, we use masked autoencoders for this one-sample learning problem. Empirically, our simple method…

This paper presents a novel generative model to synthesize fluid simulations from a set of reduced parameters. A convolutional neural network is trained on a collection of discrete, parameterizable fluid simulation velocity fields. Due to…

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…

Phase-field modeling is an elegant and versatile computation tool to predict microstructure evolution in materials in the mesoscale regime. However, these simulations require rigorous numerical solutions of differential equations, which are…

When using deep, multi-layered architectures to build generative models of data, it is difficult to train all layers at once. We propose a layer-wise training procedure admitting a performance guarantee compared to the global optimum. It is…

One-step generative modeling has emerged as a leading approach to amortize the inference cost of diffusion and flow-matching models. Among distillation-free methods, MeanFlow training is notoriously unstable, with non-decreasing loss and…

Current autoencoder-based disentangled representation learning methods achieve disentanglement by penalizing the (aggregate) posterior to encourage statistical independence of the latent factors. This approach introduces a trade-off between…

Parametric time-dependent systems are of a crucial importance in modeling real phenomena, often characterized by non-linear behaviors too. Those solutions are typically difficult to generalize in a sufficiently wide parameter space while…