想要生成可变长输出的流模型？这篇提出了EFlows和EFMs，把扩张和去噪打包成一个可学操作，还能处理图和序列，挺新鲜。
现有流模型参数化受限于固定维度或序列长度。研究者提出Expanding Generative Flows (EFlows)，通过扩张插值器在维度增长分布间定义流。在此基础上提出Expanding Flow Maps (EFMs)，将任意时间步间映射分解为expand算子（增广状态空间）和transport map（推进状态），联合扩张与去噪。EFMs可恢复固定画布流模型作为特例，并扩展至离散单纯形实现变长图生成和变长序列生成。实验证明该框架使输出尺寸成为可学习的可控自由度。
Expanding Flow Maps
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.