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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.09465 |
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| _version_ | 1866908992546013184 |
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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 |