This paper introduces a new framework for non-parallel emotion conversion in speech. Our framework is based on two key contributions. First, we propose a stochastic version of the popular CycleGAN model. Our modified loss function introduces a Kullback Leibler (KL) divergence term that aligns the source and target data distributions learned by the generators, thus overcoming the limitations of sample wise generation. By using a variational approximation to this stochastic loss function, we show that our KL divergence term can be implemented via a paired density discriminator. We term this new architecture a variational CycleGAN (VCGAN). Second, we model the prosodic features of target emotion as a smooth and learnable deformation of the source prosodic features. This approach provides implicit regularization that offers key advantages in terms of better range alignment to unseen and out of distribution speakers. We conduct rigorous experiments and comparative studies to demonstrate that our proposed framework is fairly robust with high performance against several state-of-the-art baselines.