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Discrete diffusion models have recently emerged as strong alternatives to autoregressive language models, matching their performance through large-scale training. However, inference-time control remains relatively underexplored. In this…

Discrete diffusion models have recently emerged as a powerful class of generative models for chemistry and biology data. In these fields, the goal is to generate various samples with high rewards (e.g., drug-likeness in molecules), making…

Large Language Models (LLMs) excel in diverse tasks but often underperform in specialized fields due to limited domain-specific or proprietary corpus. Continual pre-training (CPT) enhances LLM capabilities by imbuing new domain-specific or…

Every probability distribution can be approximated up to a given precision by a phase-type distribution, i.e. a distribution encoded by a continuous time Markov chain (CTMC). However, an excessive number of states in the corresponding CTMC…

Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…

Can continuous diffusion models bring the same performance breakthrough on natural language they did for image generation? To circumvent the discrete nature of text data, we can simply project tokens in a continuous space of embeddings, as…

This paper studies the rate of convergence of a family of continuous-time Markov chains (CTMC) to a mean-field model. When the mean-field model is a finite-dimensional dynamical system with a unique equilibrium point, an analysis based on…

Motivated by queues with many servers, we study Brownian steady-state approximations for continuous time Markov chains (CTMCs). Our approximations are based on diffusion models (rather than a diffusion limit) whose steady-state, we prove,…

Current state-of-the-art text generators build on powerful language models such as GPT-2, achieving impressive performance. However, to avoid degenerate text, they require sampling from a modified softmax, via temperature parameters or…

Neural Text-to-Speech (TTS) systems find broad applications in voice assistants, e-learning, and audiobook creation. The pursuit of modern models, like Diffusion Models (DMs), holds promise for achieving high-fidelity, real-time speech…

Discrete diffusion models offer a promising alternative to autoregressive generation through parallel decoding, but they suffer from a sampling wall: once categorical sampling occurs, rich distributional information collapses into one-hot…

Diffusion Language Models (DLMs) promise parallel generation and bidirectional context, yet they underperform autoregressive (AR) models in both likelihood modeling and generated text quality. We identify that this performance gap arises…

Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement…

Despite Flow Matching and diffusion models having emerged as powerful generative paradigms for continuous variables such as images and videos, their application to high-dimensional discrete data, such as language, is still limited. In this…

Machine learning models are increasingly trained or fine-tuned on synthetic data. Recursively training on such data has been observed to significantly degrade performance in a wide range of tasks, often characterized by a progressive drift…

Inference-time scaling has achieved remarkable success in language models, yet its adaptation to diffusion models remains underexplored. We observe that the efficacy of recent Sequential Monte Carlo (SMC)-based methods largely stems from…

Branching processes are a class of continuous-time Markov chains (CTMCs) with ubiquitous applications. A general difficulty in statistical inference under partially observed CTMC models arises in computing transition probabilities when the…

Self-conditioning has been central to the success of continuous diffusion language models, as it allows models to correct previous errors. Yet its ability degrades precisely in the regime where diffusion is most attractive for deployment:…

Diffusion Language Models (DLMs) have recently achieved significant success due to their any-order generation capabilities. However, existing inference methods typically rely on local, immediate-step metrics such as confidence or entropy…

We identify empirical scaling laws for the cross-entropy loss in four domains: generative image modeling, video modeling, multimodal image$\leftrightarrow$text models, and mathematical problem solving. In all cases autoregressive…