Adaptive loss function formulation is an active area of research and has gained a great deal of popularity in recent years, following the success of deep learning. However, existing frameworks of adaptive loss functions often suffer from slow convergence and poor choice of weights for the loss components. Traditionally, the elements of a multi-part loss function are weighted equally or their weights are determined through heuristic approaches that yield near-optimal (or sub-optimal) results. To address this problem, we propose a family of methods, called SoftAdapt, that dynamically change function weights for multi-part loss functions based on live performance statistics of the component losses. SoftAdapt is mathematically intuitive, computationally efficient and straightforward to implement. In this paper, we present the mathematical formulation and pseudocode for SoftAdapt, along with results from applying our methods to image reconstruction (Sparse Autoencoders) and synthetic data generation (Introspective Variational Autoencoders).