Yu Sun

Yansong Gao, Yu Sun

Discrete diffusion models (DDMs) are a powerful class of generative models for categorical data, but they typically require many function evaluations for a single sample, making inference expensive. Existing acceleration methods either rely on approximate simulators, such as $τ$-leaping, or on distillation schemes that train new student models and auxiliary networks with proxy objectives. We propose a simple and principled distillation alternative based on \emph{conditional distribution matching}. Our key observation is that the reverse conditional distribution of clean data given a noisy state, $p_{0\mid t}(x_0 \mid x_t)$, admits a Markov decomposition through intermediate times and can be recovered from marginal density ratios and the known forward CTMC kernel. We exploit this structure to define distillation objectives that directly match conditional distributions between a pre-trained teacher and a low-NFE student, both for one-step and few-step samplers.

Aoqian Zhang, Shaoxu Song, Yu Sun et al.

Missing numerical values are prevalent, e.g., owing to unreliable sensor reading, collection and transmission among heterogeneous sources. Unlike categorized data imputation over a limited domain, the numerical values suffer from two issues: (1) sparsity problem, the incomplete tuple may not have sufficient complete neighbors sharing the same/similar values for imputation, owing to the (almost) infinite domain; (2) heterogeneity problem, different tuples may not fit the same (regression) model. In this study, enlightened by the conditional dependencies that hold conditionally over certain tuples rather than the whole relation, we propose to learn a regression model individually for each complete tuple together with its neighbors. Our IIM, Imputation via Individual Models, thus no longer relies on sharing similar values among the k complete neighbors for imputation, but utilizes their regression results by the aforesaid learned individual (not necessary the same) models. Remarkably, we show that some existing methods are indeed special cases of our IIM, under the extreme settings of the number l of learning neighbors considered in individual learning. In this sense, a proper number l of neighbors is essential to learn the individual models (avoid over-fitting or under-fitting). We propose to adaptively learn individual models over various number l of neighbors for different complete tuples. By devising efficient incremental computation, the time complexity of learning a model reduces from linear to constant. Experiments on real data demonstrate that our IIM with adaptive learning achieves higher imputation accuracy than the existing approaches.