Related papers: Score matching for bridges without learning time-r…

The paper proposes a new algorithm called SymBa that aims to achieve more biologically plausible learning than Back-Propagation (BP). The algorithm is based on the Forward-Forward (FF) algorithm, which is a BP-free method for training…

Recent studies have demonstrated that the forward diffusion process is crucial for the effectiveness of diffusion models in terms of generative quality and sampling efficiency. We propose incorporating an analytical image attenuation…

Discrete diffusion models are a powerful class of generative models with strong performance across many domains. For efficiency, however, discrete diffusion typically parameterizes the generative (reverse) process with factorized…

Deep generative models have gained recent traction in accelerated MRI reconstruction. Diffusion priors are particularly promising given their representational fidelity. Instead of the target transformation from undersampled to fully-sampled…

We review the problem of finding paths in Cayley graphs of groups and group actions, using the Rubik's cube as an example, and we list several more examples of significant mathematical interest. We then show how to formulate these problems…

Diffusions are a fundamental class of models in many fields, including finance, engineering, and biology. Simulating diffusions is challenging as their sample paths are infinite-dimensional and their transition functions are typically…

Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase. Despite a flurry of recent activities towards…

Motivated by entropic optimal transport, time reversal of diffusion processes is revisited. An integration by parts formula is derived for the carr\'e du champ of a Markov process in an abstract space. It leads to a time reversal formula…

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…

Score-based distillation methods (e.g., variational score distillation) train one-step diffusion models by first pre-training a teacher score model and then distilling it into a one-step student model. However, the gradient estimator in the…

Diffusion models are an important tool for generative modelling, serving as effective priors in applications such as imaging and protein design. A key challenge in applying diffusion models for downstream tasks is efficiently sampling from…

Diffusion bridge models have shown great promise in image restoration by explicitly connecting clean and degraded image distributions. However, they often rely on complex and high-cost trajectories, which limit both sampling efficiency and…

Recent advances in powerful pre-trained diffusion models encourage the development of methods to improve the sampling performance under well-trained diffusion models. This paper introduces Diffusion Rejection Sampling (DiffRS), which uses a…

Causal discovery is a crucial initial step in establishing causality from empirical data and background knowledge. Numerous algorithms have been developed for this purpose. Among them, the score-matching method has demonstrated superior…

Diffusion-based robot navigation policies trained on large-scale imitation learning datasets, can generate multi-modal trajectories directly from the robot's visual observations, bypassing the traditional localization-mapping-planning…

Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or…

Recently Diffusion-based Purification (DiffPure) has been recognized as an effective defense method against adversarial examples. However, we find DiffPure which directly employs the original pre-trained diffusion models for adversarial…

Flow matching has recently emerged as a promising alternative to diffusion-based generative models, particularly for text-to-image generation. Despite its flexibility in allowing arbitrary source distributions, most existing approaches rely…

This is a survey paper about reciprocal processes. The bridges of a Markov process are also Markov. But an arbitrary mixture of these bridges fails to be Markov in general. However, it still enjoys the interesting properties of a reciprocal…

Diffusion-based speech enhancement has shown promising results, but can suffer from a slower inference time. Initializing the diffusion process with the enhanced audio generated by a regression-based model can be used to reduce the…