Paper Overview
- Field: Machine Learning
- Authors: Sophia Tang, Pranam Chatterjee
- Published: 2026-07-24
- arXiv: 2507.19317
- Variable-size graph generation
- Variable-length sequence generation
- arXiv: https://arxiv.org/abs/2507.19317
Summary
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. This paper introduces 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, the authors 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:
1. Expand operator — augments the state space with new coordinates or tokens conditioned on the current state. 2. Transport map — advances the expanded state forward along the interpolant.
Composing these operations yields 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.
The framework is further extended to the discrete simplex, enabling:
Across continuous and discrete modalities, EFlows and EFMs establish a principled framework in which output size itself is a learnable, controllable degree of freedom.
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