Related papers: Riemannian MeanFlow
Learning the distribution of data on Riemannian manifolds is crucial for modeling data from non-Euclidean space, which is required by many applications in diverse scientific fields. Yet, existing generative models on manifolds suffer from…
Generative modeling techniques such as Diffusion and Flow Matching have achieved significant successes in generating designable and diverse protein backbones. However, many current models are computationally expensive, requiring hundreds or…
Flow-based image generative models exhibit stable training and produce high quality samples when using multi-step sampling procedures. One-step generative models can produce high quality image samples but can be difficult to optimize as…
We present a comprehensive comparative study of three generative modeling paradigms: Denoising Diffusion Probabilistic Models (DDPM), Conditional Flow Matching (CFM), and MeanFlow. While DDPM and CFM require iterative sampling, MeanFlow…
Recently, studies on machine learning have focused on methods that use symmetry implicit in a specific manifold as an inductive bias. Grassmann manifolds provide the ability to handle fundamental shapes represented as shape spaces, enabling…
Diffusion-based visuomotor policies excel at learning complex robotic tasks by effectively combining visual data with high-dimensional, multi-modal action distributions. However, diffusion models often suffer from slow inference due to…
Generative models based on dynamical equations such as flows and diffusions offer exceptional sample quality, but require computationally expensive numerical integration during inference. The advent of consistency models has enabled…
Deploying pretrained visual models in real-world environments often suffers from significant performance degradation due to the diversity of testing scenarios. Continuous adaptation of learning models on edge devices via unlabeled data…
MeanFlow promises high-quality generative modeling in few steps, by jointly learning instantaneous and average velocity fields. Yet, the underlying training dynamics remain unclear. We analyze the interaction between the two velocities and…
Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…
We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…
Consistency models are a class of generative models that enable few-step generation for diffusion and flow matching models. While consistency models have achieved promising results on Euclidean domains like images, their applications to…
We present FrameFlow, a method for fast protein backbone generation using SE(3) flow matching. Specifically, we adapt FrameDiff, a state-of-the-art diffusion model, to the flow-matching generative modeling paradigm. We show how flow…
We present Functional Mean Flow (FMF) as a one-step generative model defined in infinite-dimensional Hilbert space. FMF extends the one-step Mean Flow framework to functional domains by providing a theoretical formulation for Functional…
Graph-structured data jointly contain discrete topology and continuous geometry, which poses fundamental challenges for generative modeling due to heterogeneous distributions, incompatible noise dynamics, and the need for equivariant…
We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications. Existing…
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…
We consider the problem of density estimation on Riemannian manifolds. Density estimation on manifolds has many applications in fluid-mechanics, optics and plasma physics and it appears often when dealing with angular variables (such as…
Controlling generative models is computationally expensive. This is because optimal alignment with a reward function--whether via inference-time steering or fine-tuning--requires estimating the value function. This task demands access to…
Generating high-quality time-series data is challenging because real-world signals often exhibit multimodal patterns and multiscale dynamics, including oscillations and high-frequency variations. Flow Matching (FM) offers an efficient…