A new framework called Expanding Generative Flows (EFlows) and its distilled version, Expanding Flow Maps (EFMs), have been introduced by researchers. These methods overcome a key limitation of existing flow-based generative models, which are typically constrained to fixed dimensions or sequence lengths. The new approach allows generative models to handle distributions with increasing dimensionality, enabling the generation of outputs with variable sizes.
Traditional flow-based generative models operate on a fixed "canvas," meaning they are designed for data of a specific, unchangeable dimension or sequence length. This limitation hinders their application in scenarios where the output size is itself a variable to be modeled, such as generating molecular structures of varying complexity, creating audio or video of arbitrary duration, or producing text of unknown length. EFlows and EFMs address this by treating output size as a learned degree of freedom.
The core innovation lies in defining flows between distributions of increasing dimensionality. This is achieved through an "expanding interpolant" that grows the state by augmenting it with conditional noise. Building on this, Expanding Flow Maps (EFMs) distill this expanding interpolant into efficient generative models that require fewer steps to produce results.
Each EFM is designed to factor the transformation between any two time steps into two distinct, learnable operations. The first is an "expand operator," which increases the state space by adding new coordinates or tokens, conditioned on the current state. The second is a "transport map," which moves the augmented state forward along the interpolant. By composing these operators, a single map is created that simultaneously expands and refines the state. This approach recovers existing fixed-dimension flow maps as a special case where the expand operator is effectively an identity function.
The framework has been extended to handle discrete data, enabling the generation of variable-sized graphs and sequences. This is achieved by extending the framework to the discrete simplex. The researchers propose that EFlows and EFMs provide a principled method for generative tasks where the output size is a controllable aspect that can be learned, rather than being predetermined.
The research demonstrates that this framework can successfully generate high-quality outputs across various domains, including molecular conformer generation, molecular graph generation, and variable-length language modeling. In many cases, these models achieve competitive or superior results compared to existing methods, often with fewer sampling steps.
The paper introducing EFlows and EFMs was authored by Sophia Tang and Pranam Chatterjee.