*Molecular dynamics* (MD) simulation is a widely used technique to simulate molecular systems, most commonly at the all-atom resolution where equations of motion are integrated with timesteps on the order of femtoseconds ($1\textrm{fs}=10^{-15}\textrm{s}$). MD is often used to compute equilibrium properties, which requires sampling from an equilibrium distribution such as the Boltzmann distribution. However, many important processes, such as binding and folding, occur over timescales of milliseconds or beyond, and cannot be efficiently sampled with conventional MD. Furthermore, new MD simulations need to be performed for each molecular system studied. We present *Timewarp*, an enhanced sampling method which uses a normalising flow as a proposal distribution in a Markov chain Monte Carlo method targeting the Boltzmann distribution. The flow is trained offline on MD trajectories and learns to make large steps in time, simulating the molecular dynamics of $10^{5} - 10^{6} \textrm{fs}$. Crucially, Timewarp is *transferable* between molecular systems: once trained, we show that it generalises to unseen small peptides (2-4 amino acids) at all-atom resolution, exploring their metastable states and providing wall-clock acceleration of sampling compared to standard MD. Our method constitutes an important step towards general, transferable algorithms for accelerating MD.

Hamiltonian Monte Carlo (HMC) is a popular sampling method in Bayesian inference. Recently, Heng & Jacob (2019) studied Metropolis HMC with couplings for unbiased Monte Carlo estimation, establishing a generic parallelizable scheme for HMC. However, in practice a different HMC method, multinomial HMC, is considered as the go-to method, e.g. as part of the no-U-turn sampler. In multinomial HMC, proposed states are not limited to end-points as in Metropolis HMC; instead points along the entire trajectory can be proposed. In this paper, we establish couplings for multinomial HMC, based on optimal transport for multinomial sampling in its transition. We prove an upper bound for the meeting time – the time it takes for the coupled chains to meet – based on the notion of local contractivity. We evaluate our methods using three targets: 1,000 dimensional Gaussians, logistic regression and log-Gaussian Cox point processes. Compared to Heng & Jacob (2019), coupled multinomial HMC generally attains a smaller meeting time, and is more robust to choices of step sizes and trajectory lengths, which allows re-use of existing adaptation methods for HMC. These improvements together paves the way for a wider and more practical use of coupled HMC methods.