How to extract as much learning signal from each trajectory data has been a key problem in reinforcement learning (RL), where sample inefficiency has posed serious challenges for practical applications. Recent works have shown that using expressive policy function approximators and conditioning on future trajectory information -- such as future states in hindsight experience replay (HER) or returns-to-go in Decision Transformer (DT) -- enables efficient learning of context-conditioned policies, where at times online RL can be fully replaced by offline behavioral cloning (BC), e.g. sequence modeling. Inspired by distributional and state-marginal matching literatures in RL, we demonstrate that all these approaches are essentially doing hindsight information matching (HIM) -- training policies that can output the rest of trajectory that matches a given future state information statistics.We first present Distributional Decision Transformer (DDT) and its practical instantiation, Categorical DT, and show that this simple modification to DT can enable effective offline state-marginal matching that generalizes well to unseen, even synthetic multi-modal, reward or state-feature distributions.We perform experiments on Gym's MuJoCo continuous control benchmarks and empirically validate performances. Additionally, we present and test another simple modification to DT called Unsupervised DT (UDT), show its connection to distribution matching, inverse RL and representation learning, and empirically demonstrate their effectiveness for offline imitation learning. To the best of our knowledge, DDT and UDT together constitute the first successes for offline state-marginal matching and inverse-RL imitation learning, allowing us to propose first benchmarks for these two important subfields and greatly expand the role of powerful sequence modeling architectures in modern RL.