Reflected UAS: Corrected Deterministic Stability and Direct CTMC Drift Calculation

We analyze Reflected UAS routing for heterogeneous multi-server queues at fixed parameters under subcritical load. The deterministic surrogate is a reflected ODE on the nonnegative orthant, not the unconstrained drift equation. This reflected ODE has a unique boundary equilibrium characterized by a scalar consistency equation and a convex-potential representation; all trajectories converge to it. The older argument lifting deterministic Lyapunov descent to CTMC stability fails: the exact generator applied to the deterministic potential produces a boundary term absent from the reflected-ODE descent identity. We give a direct Foster-Lyapunov drift inequality for the CTMC using a weighted-quadratic function, bypassing the failed lift. At the benchmark parameter point, the boundary equilibrium matches the numerical attractor to machine precision, and the default Reflected UAS policy has lower mean queue length than UAS and JSSQ across independent seed blocks.

Accelerating Discrete Diffusion Models with Parallel-In-Time Sampling

Discrete diffusion models are widely used for learning and generating discrete distributions. As the generation process is inherently sequential, the acceleration of sampling is of significant importance. In this work, we parallelize the mainstream $τ$-leaping algorithm for absorbing discrete diffusion in a Continuous-Time Markov Chain (CTMC) framework. By leveraging the continuous-time stochastic integral form of the $τ$-leaping algorithm and the Picard iteration method, we achieve parallel-in-time sampling acceleration and provide a proof of exponential-factorial convergence for our algorithm. We improve the overall time complexity of $τ$-leaping under absorbing settings from ${\mathcal{O}}(d \log S)$ to ${\mathcal{O}}(\log (d\log S)\cdot \log d)$ with respect to NFE. Empirically, our method shows consistent acceleration across synthetic and real-data settings. The new sampler achieves at most $7$--$9\times$ runtime speedup for synthetic distribution, and maintains the same quality with $50\%$ fewer NFE and $1.45$--$1.86\times$ runtime speedups in image/text tasks on a single GPU. Our research expands the potential of discrete diffusion models for efficient parallel inference, with broader implications for applications such as molecular structure and language generation.

Mask, Sample, Revise: A Revisable CTMC Inference Stack for Guided Discrete Flow Matching Text-to-Speech

Recent alignment-free non-autoregressive (NAR) text-to-speech (TTS) models formulate synthesis as a conditional infilling task, bypassing explicit duration predictors and external aligners. When speech is represented with neural codec tokens, the infilling problem becomes discrete, making Discrete Flow Matching (DFM), a Continuous-Time Markov Chain (CTMC) framework for discrete generation, a natural fit. However, inference-time control for stable low-step conditional infilling remains underexplored. We propose Mask, Sample, Revise, an inference-time CTMC stack for alignment-free DFM-TTS. The stack combines predictor-free guidance to strengthen text conditioning, prompt-matched conditional coupling to align the probability path with the acoustic prompt, and SC-ReMask, a schedule-constrained remasking mechanism that introduces token-to-mask transitions so early de-masking decisions can be revised. These components require no post-hoc fine-tuning and operate in a single tau-leaping sampler. Controlled ablations show that this stack improves intelligibility and robustness in the low-NFE prompted setting, outperforming unguided and guidance-only samplers with substantially more steps.