相关论文: Riemannian Consistency Model

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…

We describe how to approximate the Riemann curvature tensor as well as sectional curvatures on possibly infinite-dimensional shape spaces that can be thought of as Riemannian manifolds. To this end, we extend the variational time…

A fundamental dilemma in generative modeling persists: iterative diffusion models achieve outstanding fidelity, but at a significant computational cost, while efficient few-step alternatives are constrained by a hard quality ceiling. This…

Low-dose CT (LDCT) denoising remains an important yet challenging problem in medical imaging. Although recent learning-based methods have shown promising performance, those optimized using classical pixel-level objectives often produce…

In the domain of image-set based classification, a considerable advance has been made by representing original image sets as covariance matrices which typical lie in a Riemannian manifold. Specifically, it is a Symmetric Positive Definite…

Decentralized optimization on Riemannian manifolds is foundational for many modern machine learning and signal processing applications in which data are non-Euclidean and generated and processed in a distributed manner. Although intrinsic…

Diffusion models generate high-quality images but require dozens of forward passes. We introduce Distribution Matching Distillation (DMD), a procedure to transform a diffusion model into a one-step image generator with minimal impact on…

We introduce Efficient Motion Diffusion Model (EMDM) for fast and high-quality human motion generation. Current state-of-the-art generative diffusion models have produced impressive results but struggle to achieve fast generation without…

Low-dimensional structure in real-world data plays an important role in the success of generative models, which motivates diffusion models defined on intrinsic data manifolds. Such models are driven by stochastic differential equations…

We investigate how to generate multimodal image outputs, such as RGB, depth, and surface normals, with a single generative model. The challenge is to produce outputs that are realistic, and also consistent with each other. Our solution…

By restricting the iterate on a nonlinear manifold, the recently proposed Riemannian optimization methods prove to be both efficient and effective in low rank tensor completion problems. However, existing methods fail to exploit the easily…

Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…

Recent progress in image generation has sparked research into controlling these models through condition signals, with various methods addressing specific challenges in conditional generation. Instead of proposing another specialized…

We derive nonlinear stability results for numerical integrators on Riemannian manifolds, by imposing conditions on the ODE vector field and the step size that makes the numerical solution non-expansive whenever the exact solution is…

This paper proposes a novel general framework of Riemannian conjugate gradient methods, that is, conjugate gradient methods on Riemannian manifolds. The conjugate gradient methods are important first-order optimization algorithms both in…

The slow inference process of image diffusion models significantly degrades interactive user experiences. To address this, we introduce Diffusion Preview, a novel paradigm employing rapid, low-step sampling to generate preliminary outputs…

Restricted Boltzmann Machines (RBMs) offer a versatile architecture for unsupervised machine learning that can in principle approximate any target probability distribution with arbitrary accuracy. However, the RBM model is usually not…

The Poisson Flow Consistency Model (PFCM) is a consistency-style model based on the robust Poisson Flow Generative Model++ (PFGM++) which has achieved success in unconditional image generation and CT image denoising. Yet the PFCM can only…

From optimal transport to robust dimensionality reduction, a plethora of machine learning applications can be cast into the min-max optimization problems over Riemannian manifolds. Though many min-max algorithms have been analyzed in the…

Flow Matching has become a cornerstone of modern generative models like Stable Diffusion 3, largely due to the efficiency of its Rectified Flow (RF) variant. The success of RF hinges on iteratively learning straight trajectories, pushing…