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This paper introduces Discrete Markov Probabilistic Models (DMPMs), a novel discrete diffusion algorithm for discrete data generation. The algorithm operates in discrete bit space, where the noising process is a continuous-time Markov chain…

Recent studies suggest utilizing generative models instead of traditional auto-regressive algorithms for time series forecasting (TSF) tasks. These non-auto-regressive approaches involving different generative methods, including GAN,…

Flow-based generative models have recently shown impressive performance for conditional generation tasks, such as text-to-image generation. However, current methods transform a general unimodal noise distribution to a specific mode of the…

Dynamic networks exhibit temporal patterns that vary across different time scales, all of which can potentially affect processes that take place on the network. However, most data-driven approaches used to model time-varying networks…

Motivated by reduction of computational complexity, this work develops sign-error adaptive filtering algorithms for estimating time-varying system parameters. Different from the previous work on sign-error algorithms, the parameters are…

Asynchronous event sequence clustering aims to group similar event sequences in an unsupervised manner. Mixture models of temporal point processes have been proposed to solve this problem, but they often suffer from overfitting, leading to…

Discrete flow models offer a powerful framework for learning distributions over discrete state spaces and have demonstrated superior performance compared to the discrete diffusion models. However, their convergence properties and error…

In this work, we propose the model of timed partial orders (TPOs) for specifying workflow schedules, especially for modeling manufacturing processes. TPOs integrate partial orders over events in a workflow, specifying ``happens-before''…

Flow-based generative models have greatly improved text-to-speech (TTS) synthesis quality, but inference speed remains limited by the iterative sampling process and multiple function evaluations (NFE). The recent MeanFlow model accelerates…

Flow Matching (FM) is a simulation-free method for learning a continuous and invertible flow to interpolate between two distributions, and in particular to generate data from noise. Inspired by the variational nature of the diffusion…

Given a piece of speech and its transcript text, text-based speech editing aims to generate speech that can be seamlessly inserted into the given speech by editing the transcript. Existing methods adopt a two-stage approach: synthesize the…

The generative AI revolution has recently expanded to videos. Nevertheless, current state-of-the-art video models are still lagging behind image models in terms of visual quality and user control over the generated content. In this work, we…

Flow-based generative models have shown remarkable success in text-to-image generation, yet fine-tuning them with intermediate feedback remains challenging, especially for continuous-time flow matching models. Most existing approaches…

Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…

In this paper, we derive an approximation for throughput of TCP Compound connections under random losses. Throughput expressions for TCP Compound under a deterministic loss model exist in the literature. These are obtained assuming the…

With the revolution of generative AI, video-related tasks have been widely studied. However, current state-of-the-art video models still lag behind image models in visual quality and user control over generated content. In this paper, we…

Recent advances in generative AI have significantly enhanced image and video editing, particularly in the context of text prompt control. State-of-the-art approaches predominantly rely on diffusion models to accomplish these tasks. However,…

Large-scale text-to-image generative models have been a ground-breaking development in generative AI, with diffusion models showing their astounding ability to synthesize convincing images following an input text prompt. The goal of image…

These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…

The Markov-modulated Poisson process is utilised for count modelling in a variety of areas such as queueing, reliability, network and insurance claims analysis. In this paper, we extend the Markov-modulated Poisson process framework through…