We propose a new Stein self-repulsive dynamics for obtaining diversified samples from intractable un-normalized distributions. Our idea is to introduce Stein variational gradient as a repulsive force to push the samples of Langevin dynamics away from the past trajectories. This simple idea allows us to significantly decrease the auto-correlation in Langevin dynamics and hence increase the effective sample size. Importantly, as we establish in our theoretical analysis, the asymptotic stationary distribution remains correct even with the addition of the repulsive force, thanks to the special properties of the Stein variational gradient. We perform extensive empirical studies of our new algorithm, showing that our method yields much higher sample efficiency and better uncertainty estimation than vanilla Langevin dynamics.
I have the rebuttal of the authors, the paper improved indeed and some point on role of M is better clarified now although it is still a bit convoluted. The paper would be stronger if the analysis shows any theoretical advantage to the presented method. I think the author put a good effort in addressing some of my concerns and I m raising my score to 6. 
 
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Summary of the paper:
The paper proposes stein self repulsive dynamics for sampling from an unnormalized distribution. The method starts by using Langevin dynamic for up to time $Mc$ and then uses those pasts samples to guide the trajectories of the langevin sampling to explore new areas of the densities  using the stein witness function between the current particles  and the past samples( similar to Stein Variational gradient descent). 
The paper analyses the mixing properties under standard assumptions of the potential of the Boltzmann distribution and the kernel used in the Stein discrepancy, and shows convergence to the boltzman distribution as the number of particles goes to infinity and the step size goes to zero. 
Authors validate their methods and show that it indeed explores on a synthetic example new areas wrt to pure langevin dynamics. Applications in sampling from the posterior of bayesian neural networks and contextual bandits compare the performance of the proposed method to langevin dynamic and pure stein descent favorably. 
Clarity/presentation :
The paper is well written and the intuition are well presented . 
The notation $\hat{delta}_{M} $ is not great in denoting direct measures, please using another symbol. 
My main concerns with the paper are the following:
- the definition of $\bar{\delta}_{M}$ averages only $M$ particles choosen for $M$ time stamps. Something is off here for the continuous approximation to work at each time stamp you need $N$ particles and then you have a past horizon $M$. As $M\to \infty$ this does not matter, but I think in your implementation you are considering at each time step $N$ particles and you average on a horizon of size $M$. is this correct? Please clarify?
- The theorem show only asymptotic behavior and don't quantify the intuition behind the paper , that the "coverage of the samples" is higher.
 Can you for instance bound the wasserstein  distance between the pure langevin and Stein Repulsive dynamic , and between SVGD and your method, as it was done in "The promises and pitfalls of Stochastic Gradient Langevin Dynamics". Basically you can find a coupling between trajectories of your methods and the langevin dynamics and bound the wasserstein distance between the two methods. This will be insightful to see if one would mix faster with respect to the other one.  
While the appendices of the paper are lengthy I don't think they explain the most selling point of the method, since they are asymptotic and there is a confusion between the time horizon for the past , and the number of particles.  if $M$ is  $\infty$ in this defintion , we are just running langevin dynamic, and not using Stein witness function. I see an important issue in this definition of the time horizon, I think this time horizon should be finite, and that from time steps less we sample N particles , and we let this $N$ go to infinity.