We introduce the Glauber Generative Model (GGM), a new class of discrete diffusion models, to obtain new samples from a distribution given samples from a discrete space. GGM deploys a discrete Markov chain called the heat bath dynamics (or the Glauber dynamics) to denoise a sequence of noisy tokens to a sample from a joint distribution of discrete tokens. Our novel conceptual framework provides an exact reduction of the task of learning the denoising Markov chain to solving a class of binary classification tasks. More specifically, the model learns to classify a given token in a noisy sequence as signal or noise. In contrast, prior works on discrete diffusion models either solve regression problems to learn importance ratios, or minimize loss functions given by variational approximations. We apply GGM to language modeling and image generation, where images are discretized using image tokenizers like VQGANs. We show that it outperforms existing discrete diffusion models in language generation, and demonstrates strong performance for image generation without using dataset-specific image tokenizers. We also show that our model is capable of performing well in zero-shot control settings like text and image infilling.

Some key applications in medical image segmentation involve object complexes having specific topologies, but typical deep neural networks (DNNs) ignore such topologies. We propose a novel DNN framework to model topology-constrained object boundaries, incorporating both individual-object and multi-object topology constraints. Unlike typical DNNs, our topology-constrained DNN makes the learning significantly more robust to out-of-distribution images. Moreover, our DNN combines variational modeling in latent-space with uncertainty modeling of boundary points along with inter-point correlations. Results on publicly available datasets show our framework to outperform existing methods.

We present CTreeOT, a convergent, differentiable algorithm for matching two trees when each tree is conditioned on some input. Such conditional tree matching is useful for light-weight, few-shot adaptation of tree prediction models without parameter fine-tuning. CTreeOT includes an alignment algorithm that extends the popular Sinkhorn algorithm for matching tree nodes while supporting constraints on tree edges. The algorithm involves alternating between matrix rescaling and message passing updates, and can be efficiently expressed as GPU tensor operations. The second part of CTreeOT is fine-grained relevance-based reweighting of nodes that makes the match scores useful for prediction tasks. We demonstrate the usefulness of CTreeOT for cross-schema adaptation of Text-to-SQL, a popular semantic parsing task. We show that compared to state-of-the-art methods, we achieve significant increase in adaptation accuracy.