Oscar Davis

Daan Roos, Oscar Davis, Floor Eijkelboom et al.

We introduce Categorical Flow Maps, a flow-matching method for accelerated few-step generation of categorical data via self-distillation. Building on recent variational formulations of flow matching and the broader trend towards accelerated inference in diffusion and flow-based models, we define a flow map towards the simplex that transports probability mass toward a predicted endpoint, yielding a parametrisation that naturally constrains model predictions. Since our trajectories are continuous rather than discrete, Categorical Flow Maps can be trained with existing distillation techniques, as well as a new objective based on endpoint consistency. This continuous formulation also automatically unlocks test-time inference: we can directly reuse existing guidance and reweighting techniques in the categorical setting to steer sampling toward downstream objectives. Empirically, we achieve state-of-the-art few-step results on images, molecular graphs, and text, with strong performance even in single-step generation.

Oscar Davis, Anastasiia Filippova, Pierre Ablin et al.

Continuous diffusion and flow matching models could represent a powerful alternative to autoregressive approaches for language modelling (LM), as they unlock a host of advantages currently reserved for continuous modalities, including accelerated sampling and tilting. Recently, several works have demonstrated the possibility of generating discrete data continuously by a simple flow matching process between a Gaussian and the one-hot encoded data distribution. They have further shown the feasibility of accelerated sampling via Categorical Flow Maps (CFMs), resulting in competitive sample quality in the few-step regime. However, this method had only been evaluated at relatively modest scales ($<1$B), leaving the question of its scalability completely open. In this article, we train a $1.7$B-parameter base flow model on $2.1$T tokens and self-distill it into a CFM that generates diverse, high-quality text in as few as $4$ inference steps while maintaining near-data-level token entropy. Furthermore, we introduce a likelihood bound for CFMs in the semi-discrete setting, and show that they can be used to score the model on standard LM benchmarks, achieving results in the same range as discrete diffusion methods. Finally, we uncover some of the challenges that arise from training these models at scale, and we provide prescriptive insights on loss weighting and time scheduling.

Oscar Davis, Samuel Kessler, Mircea Petrache et al.

Generative modeling over discrete data has recently seen numerous success stories, with applications spanning language modeling, biological sequence design, and graph-structured molecular data. The predominant generative modeling paradigm for discrete data is still autoregressive, with more recent alternatives based on diffusion or flow-matching falling short of their impressive performance in continuous data settings, such as image or video generation. In this work, we introduce Fisher-Flow, a novel flow-matching model for discrete data. Fisher-Flow takes a manifestly geometric perspective by considering categorical distributions over discrete data as points residing on a statistical manifold equipped with its natural Riemannian metric: the $\textit{Fisher-Rao metric}$. As a result, we demonstrate discrete data itself can be continuously reparameterised to points on the positive orthant of the $d$-hypersphere $\mathbb{S}^d_+$, which allows us to define flows that map any source distribution to target in a principled manner by transporting mass along (closed-form) geodesics of $\mathbb{S}^d_+$. Furthermore, the learned flows in Fisher-Flow can be further bootstrapped by leveraging Riemannian optimal transport leading to improved training dynamics. We prove that the gradient flow induced by Fisher-Flow is optimal in reducing the forward KL divergence. We evaluate Fisher-Flow on an array of synthetic and diverse real-world benchmarks, including designing DNA Promoter, and DNA Enhancer sequences. Empirically, we find that Fisher-Flow improves over prior diffusion and flow-matching models on these benchmarks.

Oscar Davis, Michael S. Albergo, Nicholas M. Boffi et al.

Geometric data and purpose-built generative models on them have become ubiquitous in high-impact deep learning application domains, ranging from protein backbone generation and computational chemistry to geospatial data. Current geometric generative models remain computationally expensive at inference -- requiring many steps of complex numerical simulation -- as they are derived from dynamical measure transport frameworks such as diffusion and flow-matching on Riemannian manifolds. In this paper, we propose Generalised Flow Maps (GFM), a new class of few-step generative models that generalises the Flow Map framework in Euclidean spaces to arbitrary Riemannian manifolds. We instantiate GFMs with three self-distillation-based training methods: Generalised Lagrangian Flow Maps, Generalised Eulerian Flow Maps, and Generalised Progressive Flow Maps. We theoretically show that GFMs, under specific design decisions, unify and elevate existing Euclidean few-step generative models, such as consistency models, shortcut models, and meanflows, to the Riemannian setting. We benchmark GFMs against other geometric generative models on a suite of geometric datasets, including geospatial data, RNA torsion angles, and hyperbolic manifolds, and achieve state-of-the-art sample quality for single- and few-step evaluations, and superior or competitive log-likelihoods using the implicit probability flow.

Danyal Rehman, Oscar Davis, Jiarui Lu et al.

Simulation-free training frameworks have been at the forefront of the generative modelling revolution in continuous spaces, leading to large-scale diffusion and flow matching models. However, such modern generative models suffer from expensive inference, inhibiting their use in numerous scientific applications like Boltzmann Generators (BGs) for molecular conformations that require fast likelihood evaluation. In this paper, we revisit classical normalizing flows in the context of BGs that offer efficient sampling and likelihoods, but whose training via maximum likelihood is often unstable and computationally challenging. We propose Regression Training of Normalizing Flows (RegFlow), a novel and scalable regression-based training objective that bypasses the numerical instability and computational challenge of conventional maximum likelihood training in favour of a simple $\ell_2$-regression objective. Specifically, RegFlow maps prior samples under our flow to targets computed using optimal transport couplings or a pre-trained continuous normalizing flow (CNF). To enhance numerical stability, RegFlow employs effective regularization strategies such as a new forward-backward self-consistency loss that enjoys painless implementation. Empirically, we demonstrate that RegFlow unlocks a broader class of architectures that were previously intractable to train for BGs with maximum likelihood. We also show RegFlow exceeds the performance, computational cost, and stability of maximum likelihood training in equilibrium sampling in Cartesian coordinates of alanine dipeptide, tripeptide, and tetrapeptide, showcasing its potential in molecular systems.