Generative Model via Quantile Assignment

Deep Generative models (DGMs) play two key roles in modern machine learning: (i) producing new information (e.g., image synthesis) and (ii) reducing dimensionality. However, traditional architectures often rely on auxiliary networks such as encoders in Variational Autoencoders (VAEs) or discriminators in Generative Adversarial Networks (GANs), which introduce training instability, computational overhead, and risks like mode collapse. In this work, we present NeuroSQL, a new generative paradigm that eliminates the need for auxiliary networks by learning low-dimensional latent representations implicitly. NeuroSQL leverages an asymptotic approximation that expresses the latent variables as the solution to an optimal transportation problem. Specifically, NeuroSQL learns the latent variables by solving a linear assignment problem and then passes the latent information to a standalone generator. To demonstrate NeuroSQL's efficacy, we benchmark its performance against GANs, VAEs, and a budget-matched diffusion baseline on four independent datasets on handwritten digits (MNIST), faces from the CelebFaces Attributes Dataset (CelebA), animal faces from Animal Faces HQ (AFHQ), and brain images from the Open Access Series of Imaging Studies (OASIS). Compared to VAEs, GANs, and diffusion models: (1) in terms of image quality, NeuroSQL achieves overall lower mean pixel distance between synthetic and authentic images and stronger perceptual/structural fidelity, under the same computational setting; (2) computationally, NeuroSQL requires the least amount of training time; and (3) practically, NeuroSQL provides an effective solution for generating synthetic data when there are limited training data (e.g., data with a higher-dimensional feature space than the sample size). Taken together, by embracing quantile assignment rather than an encoder, NeuroSQL provides a fast, stable, and robust way to generate synthetic data with minimal information loss.