Summary
Expanding Flow Maps (EFMs), by Sophia Tang and Pranam Chatterjee (arXiv:2507.19317), address a key limitation of flow-based generative models: existing parameterizations are constrained to fixed dimensions or fixed sequence lengths. The authors first introduce Expanding Generative Flows (EFlows), which define flows between distributions of increasing dimensionality via an expanding interpolant that grows the state by augmenting it with conditional noise. Building on this, EFMs 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, and a transport map, which advances the expanded state along the interpolant. Composing these yields a single map that jointly expands and denoises the state, recovering existing fixed-canvas flows and flow maps as special cases where the expand operator is the identity. The framework extends to the discrete simplex, enabling variable-size graph generation and variable-length sequence generation. Across continuous and discrete modalities, EFlows and EFMs establish output size as a learnable, controllable degree of freedom within a principled framework.
Paper Overview
Research Area: Machine Learning
Authors: Sophia Tang, Pranam Chatterjee
Published: 2026-07-24
arXiv: 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:
- Expand operator: augments the state space with new coordinates or tokens, conditioned on the current state.
- Transport map: advances the expanded state forward along the interpolant.
Composing these operations yields a single map that jointly expands and denoises the state, recovering existing fixed-canvas flows and flow maps as special cases where the expand operator is the identity mapping.
The framework further extends to the discrete simplex, enabling:
- Variable-size graph generation
- Variable-length sequence generation
Across both continuous and discrete modalities, EFlows and EFMs establish output size as a learnable, controllable degree of freedom within a principled framework.
Links
- Paper: https://arxiv.org/abs/2507.19317
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