AI summaryⓘ
The authors introduce Expanding Generative Flows (EFlows), a new method for generating data that can grow in size or length, unlike previous models limited to fixed dimensions or lengths. Their approach builds flows between distributions that increase in size by adding conditional noise. They also propose Expanding Flow Maps (EFMs), which break down the generation process into two steps: expanding the data space with new parts and moving the data forward while cleaning it up. This framework works for both continuous data (like images) and discrete data (like graphs or sequences) and allows the model to control output size as part of learning. Existing fixed-size flow models are shown as a special case within their broader approach.
generative modelsflow-based modelsdimensionality expansionconditional noiseexpand operatortransport mapcontinuous datadiscrete datavariable-length sequencesgraph generation
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, and a transport map, which pushes the expanded state forward along the interpolant. Composing these operators yields a single map that jointly expands and denoises the state, recovering existing fixed-canvas flows and flow maps as the special case in which the expand operator is the identity. We further extend the framework to the discrete simplex, enabling variable-size graph generation and variable-length sequence generation. Across both continuous and discrete modalities, we establish EFlows and EFMs as a principled framework for settings in which output size is itself a learned, controllable degree of freedom.