Discrete diffusion models are often trained through clean-data prediction, but the prediction can be used in different ways to define the reverse dynamics. In Masked Diffusion Models (MDM) these choices largely coincide, whereas in Uniform Diffusion Models (UDM) they do not. We show that the standard plug-in bridge parameterization for UDM is not optimized by the denoising posterior, but by a leave-one-out posterior that predicts each clean token without using its own noisy observation. This identifies a mismatch between the plug-in ELBO and the usual cross-entropy denoising objective. We characterize the leave-one-out target and derive exact conversions between the denoiser, the leave-one-out posterior, and the score. These conversions allow us to disentangle parameterization and training objective. Our results also lead to inference improvements without any additional training through an informed predictor-corrector sampler and improved temperature sampling based on the leave-one-out predictor. We further introduce an absorbing-state reformulation of uniform diffusion that preserves the UDM joint law while decomposing it into masked-diffusion-like sampling operations, with simpler denoising posteriors, carry-over unmasking, and a natural remasking mechanism. On language modeling, leave-one-out parameterizations consistently improve UDM generation, while the absorbing construction matches or surpasses masked diffusion. These results suggest that the empirical gap between masked and uniform diffusion is driven less by the choice of marginals themselves than by parameterization and sampling design. The code and models can be found at https://github.com/samsongourevitch/rev_udm.

Recent advances in dysfluency detection have introduced a variety of modeling paradigms, ranging from lightweight object-detection inspired networks (YOLOStutter) to modular interpretable frameworks (UDM). While performance on benchmark datasets continues to improve, clinical adoption requires more than accuracy: models must be controllable and explainable. In this paper, we present a systematic comparative analysis of four representative approaches--YOLO-Stutter, FluentNet, UDM, and SSDM--along three dimensions: performance, controllability, and explainability. Through comprehensive evaluation on multiple datasets and expert clinician assessment, we find that YOLO-Stutter and FluentNet provide efficiency and simplicity, but with limited transparency; UDM achieves the best balance of accuracy and clinical interpretability; and SSDM, while promising, could not be fully reproduced in our experiments. Our analysis highlights the trade-offs among competing approaches and identifies future directions for clinically viable dysfluency modeling. We also provide detailed implementation insights and practical deployment considerations for each approach.

Humans are universal decision makers: we reason causally to understand the world; we act competitively to gain advantage in commerce, games, and war; and we are able to learn to make better decisions through trial and error. In this paper, we propose Universal Decision Model (UDM), a mathematical formalism based on category theory. Decision objects in a UDM correspond to instances of decision tasks, ranging from causal models and dynamical systems such as Markov decision processes and predictive state representations, to network multiplayer games and Witsenhausen's intrinsic models, which generalizes all these previous formalisms. A UDM is a category of objects, which include decision objects, observation objects, and solution objects. Bisimulation morphisms map between decision objects that capture structure-preserving abstractions. We formulate universal properties of UDMs, including information integration, decision solvability, and hierarchical abstraction. We describe universal functorial representations of UDMs, and propose an algorithm for computing the minimal object in a UDM using algebraic topology. We sketch out an application of UDMs to causal inference in network economics, using a complex multiplayer producer-consumer two-sided marketplace.

We propose a learning system in which language is grounded in visual percepts without specific pre-defined categories of terms. We present a unified generative method to acquire a shared semantic/visual embedding that enables the learning of language about a wide range of real-world objects. We evaluate the efficacy of this learning by predicting the semantics of objects and comparing the performance with neural and non-neural inputs. We show that this generative approach exhibits promising results in language grounding without pre-specifying visual categories under low resource settings. Our experiments demonstrate that this approach is generalizable to multilingual, highly varied datasets.