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Diffusion models have achieved promising results on generative learning recently. However, because diffusion processes are most naturally applied on the uncon- strained Euclidean space Rd, key challenges arise for developing diffusion based models for learning data on constrained and structured domains. We present a simple and unified framework to achieve this that can be easily adopted to various types of domains, including product spaces of any type (be it bounded/unbounded, continuous/discrete, categorical/ordinal, or their mix). In our model, the diffu- sion process is driven by a drift force that is a sum of two terms: one singular force designed by Doob’s h-transform that ensures all outcomes of the process to belong to the desirable domain, and one non-singular neural force field that is trained to make sure the outcome follows the data distribution statistically. Ex- periments show that our methods perform superbly on generating tabular data, images, semantic segments and 3D point clouds. Code is available at https: //github.com/gnobitab/ConstrainedDiffusionBridge.