AI 中文总结
研究针对现有基于流的生成模型局限，提出扩展流图（EFMs），将任意两时间步映射分解为扩展算子与传输映射，能联合扩展和去噪状态，还扩展到离散单纯形，实现可变大小图与可变长度序列生成，为相关设置建立框架。
AI 中文摘要
基于流的生成模型在连续和离散状态空间的快速可控生成方面取得了显著进展，但现有参数化受限于固定维度或固定序列长度。本文引入扩展生成流（EFlows），它沿着通过条件噪声扩充状态来增长的扩展插值器，在维度增加的分布之间定义流。在此基础上提出扩展流图（EFMs），将扩展插值器提炼为高效的少步生成模型。每个EFM将任意两个时间步之间的映射分解为两个可学习操作：扩展算子和传输映射。还将框架扩展到离散单纯形，实现可变大小图生成和可变长度序列生成。在连续和离散模态中，EFlows和EFMs为输出大小是可学习、可控自由度的设置建立了一个有原则的框架。
英文摘要
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.
