We present a learning-based method (LCollision) that synthesizes collision-free 3D human poses. At the crux of our approach is a novel deep architecture that simultaneously decodes new human poses from the latent space and classifies the collision status. These two components of our architecture are used as the objective function and surrogate hard-constraints in a constrained-optimization algorithm for collision-free human pose generation. A novel aspect of our approach is the use of a bilevel autoencoder that decomposes whole-body collisions into groups of collisions between localized body parts. We show that solving our constrained optimization formulation can resolve collision artifacts neglected by prior learning algorithms. Furthermore, in a large test set of $2.5\times 10^6$ randomized poses from three major datasets, our architecture achieves a collision-prediction accuracy of $94.1\%$ with $80\times$ speedup over exact collision detection algorithms. To the best of our knowledge, LCollision is the first approach that can obtain high accuracy in terms of handling non-penetration and collision constraints in a learning framework.