Conventional imitation learning assumes access to the actions of demonstrators, but these motor signals are often non-observable in naturalistic settings.

Sampling in discrete spaces, with critical applications in simulation and opti-1 mization, has recently been boosted by significant advances in gradient-based2 approaches that exploit modern accelerators like GPUs. However, two key chal-3 lenges hinder the further research progress in discrete sampling. First, since there4 is no consensus on experimental settings, the empirical results in different research5 papers are often not comparable. Secondly, implementing samplers and target6 distributions often requires a nontrivial amount of effort in terms of calibration,7 parallelism, and evaluation. To tackle these challenges, we propose DISCS (DIS-8 Crete Sampling), a tailored package and benchmark that supports unified and9 efficient implementation and evaluations for discrete sampling in three types of10 tasks: sampling for classical graphical models, combinatorial optimization, and11 energy based generative models. Throughout the comprehensive evaluations in12 DISCS, we acquired new insights into scalability, design principles for proposal13 distributions, and lessons for adaptive sampling design.

Applying pre-trained generative denoising diffusion models (DDMs) for downstream tasks such as image semantic editing usually requires either fine-tuning DDMs or learning auxiliary editing networks in the existing literature. In this work, we present our BoundaryDiffusion method for efficient, effective and lightweight semantic control with frozen pre-trained DDMs, without learning any extra networks. As one of the first learning-free diffusion editing works, we start by seeking a comprehensive understanding of the intermediate high-dimensional latent spaces by theoretically and empirically analyzing their probabilistic and geometric behaviors in the Markov chain. We then propose to further explore the critical step for editing in the denoising trajectory that characterizes the convergence of a pre-trained DDM and introduce an automatic search method. Last but not least, in contrast to the conventional understanding that DDMs have relatively poor semantic behaviors, we prove that the critical latent space we found already exhibits semantic subspace boundaries at the generic level in unconditional DDMs, which allows us to do controllable manipulation by guiding the denoising trajectory towards the targeted boundary via a single-step operation. We conduct extensive experiments on multiple DPMs architectures (DDPM, iDDPM) and datasets (CelebA, CelebA-HQ, LSUN-church, LSUN-bedroom, AFHQ-dog) with different resolutions (64, 256), achieving superior or state-of-the-art performance in various task scenarios (image semantic editing, text-based editing, unconditional semantic control) to demonstrate the effectiveness.

Some of the most successful knowledge graph embedding (KGE) models for link prediction - CP, RESCAL, TUCKER, COMPLEX - can be interpreted as energy-based models. Under this perspective they are not amenable for exact maximum-likelihood estimation (MLE), sampling and struggle to integrate logical constraints. This work re-interprets the score functions of these KGEs as circuits - constrained computational graphs allowing efficient marginalisation. Then, we design two recipes to obtain efficient generative circuit models by either restricting their activations to be non-negative or squaring their outputs. Our interpretation comes with little or no loss of performance for link prediction, while the circuits framework unlocks exact learning by MLE, efficient sampling of new triples, and guarantee that logical constraints are satisfied by design.