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Main Authors: Billera, Lukas, Nordlinder, Hedwig Nora, Ryder, Jack Collier, Oresten, Anton, Stålmarck, Aron, Björk, Theodor Mosetti, Murrell, Ben
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2511.09465
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author Billera, Lukas
Nordlinder, Hedwig Nora
Ryder, Jack Collier
Oresten, Anton
Stålmarck, Aron
Björk, Theodor Mosetti
Murrell, Ben
author_facet Billera, Lukas
Nordlinder, Hedwig Nora
Ryder, Jack Collier
Oresten, Anton
Stålmarck, Aron
Björk, Theodor Mosetti
Murrell, Ben
contents Diffusion and flow matching approaches to generative modeling have shown promise in domains where the state space is continuous, such as image generation or protein folding & design, and discrete, exemplified by diffusion large language models. They offer a natural fit when the number of elements in a state is fixed in advance (e.g. images), but require ad hoc solutions when, for example, the length of a response from a large language model, or the number of amino acids in a protein chain is not known a priori. Here we propose Branching Flows, a generative modeling framework that, like diffusion and flow matching approaches, transports a simple distribution to the data distribution. But in Branching Flows, the elements in the state evolve over a forest of binary trees, branching and dying stochastically with rates that are learned by the model. This allows the model to control, during generation, the number of elements in the sequence. We also show that Branching Flows can compose with any flow matching base process on discrete sets, continuous Euclidean spaces, smooth manifolds, and `multimodal' product spaces that mix these components. We demonstrate this in three domains: small molecule generation (multimodal), antibody sequence generation (discrete), and protein backbone generation (multimodal), and show that Branching Flows is a capable distribution learner with a stable learning objective, and that it enables new capabilities.
format Preprint
id arxiv_https___arxiv_org_abs_2511_09465
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Branching Flows: Discrete, Continuous, and Manifold Flow Matching with Splits and Deletions
Billera, Lukas
Nordlinder, Hedwig Nora
Ryder, Jack Collier
Oresten, Anton
Stålmarck, Aron
Björk, Theodor Mosetti
Murrell, Ben
Machine Learning
Diffusion and flow matching approaches to generative modeling have shown promise in domains where the state space is continuous, such as image generation or protein folding & design, and discrete, exemplified by diffusion large language models. They offer a natural fit when the number of elements in a state is fixed in advance (e.g. images), but require ad hoc solutions when, for example, the length of a response from a large language model, or the number of amino acids in a protein chain is not known a priori. Here we propose Branching Flows, a generative modeling framework that, like diffusion and flow matching approaches, transports a simple distribution to the data distribution. But in Branching Flows, the elements in the state evolve over a forest of binary trees, branching and dying stochastically with rates that are learned by the model. This allows the model to control, during generation, the number of elements in the sequence. We also show that Branching Flows can compose with any flow matching base process on discrete sets, continuous Euclidean spaces, smooth manifolds, and `multimodal' product spaces that mix these components. We demonstrate this in three domains: small molecule generation (multimodal), antibody sequence generation (discrete), and protein backbone generation (multimodal), and show that Branching Flows is a capable distribution learner with a stable learning objective, and that it enables new capabilities.
title Branching Flows: Discrete, Continuous, and Manifold Flow Matching with Splits and Deletions
topic Machine Learning
url https://arxiv.org/abs/2511.09465