Is there any Python library available for manifold learning using diffusion map? I would like to use unsupervised learning with a technique called diffusion map based manifold learning in Python. The original paper on the diffusion map is An Introduction to Diffusion Maps.

I have already checkout pydiffmap library, but it is super slow with my use case, and I am yet to see someone endorse the correctness of the implementation. I am looking for an alternate implementation in Python or R. 

PS: It is also not available in sklearn, as far as I know. The list of other methods in sklearn is here.
The first place I would have directed you would be Sklearn and pydiffmap. I found this paper specifically about the problem you are doing using python the reference a package called  megaman  It seems like an active  Github . I suggest not just looking at manifold learning papers but leaning towards a search toward non linear embedding or non linear dimensionality reduction as well. The paper you give doesn't reference local linear embedding but seems to be similar conceptually. 

I found this   kernel pca document  which is very straight forward and I think will help you going forward as well. I believe the RBF Kernel PCA part may be of use to you at least as a way of benchmarking how well your diffusion map is functioning.