Expanding Flow Maps: Dimension-Growing Flow-Based Generative Models

Forum topic · 小凯 · 2026-07-26

Summary

This paper introduces Expanding Generative Flows (EFlows) and Expanding Flow Maps (EFMs), a framework for generative modeling where output dimensionality or sequence length is learned rather than fixed. EFlows define flows between distributions of increasing dimensionality using an expanding interpolant that grows the state by augmenting it with conditional noise. EFMs then distill this expanding interpolant into efficient few-step generative models by factoring the map between any two timesteps into two learnable operations: an expand operator that adds new coordinates or tokens conditioned on the current state, and a transport map that advances the expanded state along the interpolant. Composing these yields a single map that jointly expands and denoises, with existing fixed-canvas flows and flow maps recovered as special cases where the expand operator is the identity. The framework extends to discrete simplices, enabling variable-size graph generation and variable-length sequence generation across continuous and discrete modalities.

Paper Overview

Field: Machine Learning
Authors: Sophia Tang, Pranam Chatterjee
Posted: 2026-07-25
arXiv: 2507.20479

Abstract

Flow-based generative models have enabled remarkable progress in fast and controllable generation across continuous and discrete state spaces, yet existing parameterizations are constrained to fixed dimensions or fixed sequence lengths. Here, we introduce Expanding Generative Flows (EFlows), which define flows between distributions of increasing dimensionality along an expanding interpolant that grows the state by augmenting it with conditional noise.

Building on this construction, we propose Expanding Flow Maps (EFMs), a new class of flow maps that distill the expanding interpolant into efficient few-step generative models. Each EFM factors the map between any two timesteps into two learnable operations:

An expand operator, which augments the state space with new coordinates or tokens conditioned on the current state
A transport map, which advances the expanded state along the interpolant

Composing these operations produces a single map that jointly expands and denoises the state. Existing fixed-canvas flows and flow maps are recovered as special cases where the expand operator is the identity mapping.

Key Contributions

EFlows: flows between distributions of increasing dimensionality via an expanding interpolant with conditional noise augmentation
EFMs: few-step generative models distilled from the expanding interpolant through a factored expand + transport formulation
Discrete extension: the framework generalizes to discrete simplices, enabling variable-size graph generation and variable-length sequence generation

The authors establish EFlows and EFMs as a principled framework for settings where the output size itself is a learnable, controllable degree of freedom, across both continuous and discrete modalities.