  Despite the recent advances in the field of computational Schr\"odinger
Bridges (SB), most existing SB solvers are still heavy-weighted and require
complex optimization of several neural networks. It turns out that there is no
principal solver which plays the role of simple-yet-effective baseline for SB
just like, e.g., $k$-means method in clustering, logistic regression in
classification or Sinkhorn algorithm in discrete optimal transport. We address
this issue and propose a novel fast and simple SB solver. Our development is a
smart combination of two ideas which recently appeared in the field: (a)
parameterization of the Schr\"odinger potentials with sum-exp quadratic
functions and (b) viewing the log-Schr\"odinger potentials as the energy
functions. We show that combined together these ideas yield a lightweight,
simulation-free and theoretically justified SB solver with a simple
straightforward optimization objective. As a result, it allows solving SB in
moderate dimensions in a matter of minutes on CPU without a painful
hyperparameter selection. Our light solver resembles the Gaussian mixture model
which is widely used for density estimation. Inspired by this similarity, we
also prove an important theoretical result showing that our light solver is a
universal approximator of SBs. Furthemore, we conduct the analysis of the
generalization error of our light solver. The code for our solver can be found
at https://github.com/ngushchin/LightSB
