BenjMurrell
@benjmurrell.bsky.social
🇸🇪🇿🇦 Researcher at Karolinska. Comp bio. Phylogenetics. Deep learning. All in Julia. Virology. Immunology.
https://scholar.google.com/citations?user=I80vy5cAAAAJ
https://scholar.google.com/citations?user=I80vy5cAAAAJ
We're still newcomers in this space, and the literature is vast, so if you think we've missed something, or have any key citations to suggest, please let us know and we'll be happy to update the preprint!
November 21, 2025 at 11:09 PM
We're still newcomers in this space, and the literature is vast, so if you think we've missed something, or have any key citations to suggest, please let us know and we'll be happy to update the preprint!
(We also show this for Edit Flows, which lies just outside of Generator Matching)
arxiv.org/abs/2506.09018
arxiv.org/abs/2506.09018
Edit Flows: Flow Matching with Edit Operations
Autoregressive generative models naturally generate variable-length sequences, while non-autoregressive models struggle, often imposing rigid, token-wise structures. We propose Edit Flows, a non-autor...
arxiv.org
November 21, 2025 at 11:09 PM
(We also show this for Edit Flows, which lies just outside of Generator Matching)
arxiv.org/abs/2506.09018
arxiv.org/abs/2506.09018
This means that if you're training a flow matching or diffusion model, you can happily rescale your loss with any (positive almost everywhere and integrable) scaling function, and the theoretical guarantees from Generator Matching will still hold.
November 21, 2025 at 11:09 PM
This means that if you're training a flow matching or diffusion model, you can happily rescale your loss with any (positive almost everywhere and integrable) scaling function, and the theoretical guarantees from Generator Matching will still hold.
For this, we closely follow the incredible Generator Matching framework, which subsumes nearly all flow matching and diffusion models.
arxiv.org/abs/2410.20587
arxiv.org/abs/2410.20587
Generator Matching: Generative modeling with arbitrary Markov processes
We introduce Generator Matching, a modality-agnostic framework for generative modeling using arbitrary Markov processes. Generators characterize the infinitesimal evolution of a Markov process, which ...
arxiv.org
November 21, 2025 at 11:09 PM
For this, we closely follow the incredible Generator Matching framework, which subsumes nearly all flow matching and diffusion models.
arxiv.org/abs/2410.20587
arxiv.org/abs/2410.20587
But when we looked, we couldn't find a sufficiently general justification.
So our preprint, driven by @lukasbillera.bsky.social with assists from @hedwignordlinder.bsky.social, formalizes this, and extends it a little in ways that are trickier to heuristically reason about:
arxiv.org/abs/2511.16599
So our preprint, driven by @lukasbillera.bsky.social with assists from @hedwignordlinder.bsky.social, formalizes this, and extends it a little in ways that are trickier to heuristically reason about:
arxiv.org/abs/2511.16599
Time dependent loss reweighting for flow matching and diffusion models is theoretically justified
This brief note clarifies that, in Generator Matching (which subsumes a large family of flow matching and diffusion models over continuous, manifold, and discrete spaces), both the Bregman divergence ...
arxiv.org
November 21, 2025 at 11:09 PM
But when we looked, we couldn't find a sufficiently general justification.
So our preprint, driven by @lukasbillera.bsky.social with assists from @hedwignordlinder.bsky.social, formalizes this, and extends it a little in ways that are trickier to heuristically reason about:
arxiv.org/abs/2511.16599
So our preprint, driven by @lukasbillera.bsky.social with assists from @hedwignordlinder.bsky.social, formalizes this, and extends it a little in ways that are trickier to heuristically reason about:
arxiv.org/abs/2511.16599
We want things to be a bit less handwavey than this though, and we needed it for Branching Flows.
bsky.app/profile/benj...
bsky.app/profile/benj...
We figured out flow matching over states that change dimension. With "Branching Flows", the model decides how big things must be! This works wherever flow matching works, with discrete, continuous, and manifold states. We think this will unlock some genuinely new capabilities.
November 21, 2025 at 11:09 PM
We want things to be a bit less handwavey than this though, and we needed it for Branching Flows.
bsky.app/profile/benj...
bsky.app/profile/benj...
Intuition suggests that it should be safe to re-weight your loss differently across time. E.g. If you trained a different model for each timestep, a time-dependent scaling would just be a constant for each model, and wouldn't change what is learned.
November 21, 2025 at 11:09 PM
Intuition suggests that it should be safe to re-weight your loss differently across time. E.g. If you trained a different model for each timestep, a time-dependent scaling would just be a constant for each model, and wouldn't change what is learned.
We have antibody sequences (which you can read like text - maybe I'll pull out some sample trajectories and drop them in here) and we're getting started with text proper. Images are a less natural fit because of their grid structure!
November 10, 2025 at 1:33 PM
We have antibody sequences (which you can read like text - maybe I'll pull out some sample trajectories and drop them in here) and we're getting started with text proper. Images are a less natural fit because of their grid structure!
Remind me to show you the twitter screenshot someone pinned on the wall in my office after my first Omicron neut thread 🤣
November 10, 2025 at 12:55 PM
Remind me to show you the twitter screenshot someone pinned on the wall in my office after my first Omicron neut thread 🤣
Ah @hedwignordlinder.bsky.social is on here too!
November 10, 2025 at 9:34 AM
Ah @hedwignordlinder.bsky.social is on here too!
Oh and as usual, these visualizations (which are, to us, key to understanding these processes) were made by @antonoresten.bsky.social in @makie.org (@simi.bsky.social).
November 10, 2025 at 9:10 AM
Oh and as usual, these visualizations (which are, to us, key to understanding these processes) were made by @antonoresten.bsky.social in @makie.org (@simi.bsky.social).
With my wonderful lab, who mostly aren't on here (except @lukasbillera.bsky.social and @antonoresten.bsky.social ?) we've been tinkering in this space since the end of the summer, but we think this is just too cool to sit on any longer.
The manuscript should be up by tomorrow and I'll drop a link.
The manuscript should be up by tomorrow and I'll drop a link.
November 10, 2025 at 9:10 AM
With my wonderful lab, who mostly aren't on here (except @lukasbillera.bsky.social and @antonoresten.bsky.social ?) we've been tinkering in this space since the end of the summer, but we think this is just too cool to sit on any longer.
The manuscript should be up by tomorrow and I'll drop a link.
The manuscript should be up by tomorrow and I'll drop a link.
We've got a flexible implementation in Julia (github.com/MurrellGroup...) that uses our Flowfusion.jl package so you can compose families of base flows with the branching and deletion process. If there is community interest, we can set up a python implementation as well.
GitHub - MurrellGroup/BranchingFlows.jl
Contribute to MurrellGroup/BranchingFlows.jl development by creating an account on GitHub.
github.com
November 10, 2025 at 9:10 AM
We've got a flexible implementation in Julia (github.com/MurrellGroup...) that uses our Flowfusion.jl package so you can compose families of base flows with the branching and deletion process. If there is community interest, we can set up a python implementation as well.
Eg. here is a protein example where the model designs two domains with an intervening linker (light blue chain in vid). A regular flow model would need to know, early on, exactly how many AAs are needed in the linker, but Branching Flows can decide on-the-fly and grow or shrink it.
November 10, 2025 at 9:10 AM
Eg. here is a protein example where the model designs two domains with an intervening linker (light blue chain in vid). A regular flow model would need to know, early on, exactly how many AAs are needed in the linker, but Branching Flows can decide on-the-fly and grow or shrink it.
We dislike ad hoc padding in discrete diffusion models, and the situation is even worse in continuous domains. Branching Flows removes this blemish. We also expect that this makes the trajectories easier to learn.
November 10, 2025 at 9:10 AM
We dislike ad hoc padding in discrete diffusion models, and the situation is even worse in continuous domains. Branching Flows removes this blemish. We also expect that this makes the trajectories easier to learn.
Given that all of the deletions, trees, anchors, etc are in Z, which doesn't interact with the theory, it is easy to manipulate the trajectories the model is learning.
Autocorrelated insertions? Change how you build the trees! Same for the "anchors" which control the process on internal branches.
Autocorrelated insertions? Change how you build the trees! Same for the "anchors" which control the process on internal branches.
November 10, 2025 at 9:10 AM
Given that all of the deletions, trees, anchors, etc are in Z, which doesn't interact with the theory, it is easy to manipulate the trajectories the model is learning.
Autocorrelated insertions? Change how you build the trees! Same for the "anchors" which control the process on internal branches.
Autocorrelated insertions? Change how you build the trees! Same for the "anchors" which control the process on internal branches.
You can see the branching pattern in the static plots "with trails", and if you stare at them you can see where lineages delete too.
November 10, 2025 at 9:10 AM
You can see the branching pattern in the static plots "with trails", and if you stare at them you can see where lineages delete too.
The process can be seen clearly with a QM9-trained model (continuous atom positions, discrete atom types), starting from a single atom.
November 10, 2025 at 9:10 AM
The process can be seen clearly with a QM9-trained model (continuous atom positions, discrete atom types), starting from a single atom.
Side note: this is heavily inspired by the processes from phylogenetics (the other thing my lab works on).
November 10, 2025 at 9:10 AM
Side note: this is heavily inspired by the processes from phylogenetics (the other thing my lab works on).
The trick that makes it tractable to learn, for eg. continuous states, is that branching events are not generic insertions into space (which, we think, you need for TD jumps (@arnauddoucet.bsky.social ?). Instead, they duplicate the state that is branching.
November 10, 2025 at 9:10 AM
The trick that makes it tractable to learn, for eg. continuous states, is that branching events are not generic insertions into space (which, we think, you need for TD jumps (@arnauddoucet.bsky.social ?). Instead, they duplicate the state that is branching.
Then on the internal nodes of the trees, we place "anchor" states (same space as the X1 elements). We put all that in Z.
Then, given this Z, Xt evolves over the trees, sampling when (but not which) branching and deletion events occur, all constructed to terminate at X1.
Then, given this Z, Xt evolves over the trees, sampling when (but not which) branching and deletion events occur, all constructed to terminate at X1.
November 10, 2025 at 9:10 AM
Then on the internal nodes of the trees, we place "anchor" states (same space as the X1 elements). We put all that in Z.
Then, given this Z, Xt evolves over the trees, sampling when (but not which) branching and deletion events occur, all constructed to terminate at X1.
Then, given this Z, Xt evolves over the trees, sampling when (but not which) branching and deletion events occur, all constructed to terminate at X1.
With Branching Flows, we draw X1 from the data. Then we draw X0 (one element? many elements? it all works). Then we add "to-be-deleted" nodes into X1. Then we draw a forest of trees, one per X0 element, that maps (one to many) the X0 elements to all the X1s (plus to-be-deleteds).
November 10, 2025 at 9:10 AM
With Branching Flows, we draw X1 from the data. Then we draw X0 (one element? many elements? it all works). Then we add "to-be-deleted" nodes into X1. Then we draw a forest of trees, one per X0 element, that maps (one to many) the X0 elements to all the X1s (plus to-be-deleteds).
Typically Z will include X0 from an easy-to-sample distribution and X1 from the data distribution, and if you're feeling fancy you might couple them ( @alextong.bsky.social ). But what we learned while working on Branching Flows is that Z is a *playground*.
November 10, 2025 at 9:10 AM
Typically Z will include X0 from an easy-to-sample distribution and X1 from the data distribution, and if you're feeling fancy you might couple them ( @alextong.bsky.social ). But what we learned while working on Branching Flows is that Z is a *playground*.
How does this work? First, you need to understand the amazing Generator Matching (arxiv.org/abs/2410.20587). In GM you first sample Z, and then construct a stochastic process Xt that, conditioned on Z, terminates at the data distribution.
November 10, 2025 at 9:10 AM
How does this work? First, you need to understand the amazing Generator Matching (arxiv.org/abs/2410.20587). In GM you first sample Z, and then construct a stochastic process Xt that, conditioned on Z, terminates at the data distribution.