Machine learning (ML) has emerged in recent years as a data-driven approach for photonic inverse design. Despite their impressive performance in finding abstract mappings between the design parameters and optical properties, ML algorithms suffer from a high likelihood of slow converging when there exist multiple designs giving similar optical responses. Here we adopt a deep convolutional mixture density neural network, which models the design as a mixture of Gaussian distributions rather than discrete values, to address the non-uniqueness issue. An example of layered structures consisting of alternating oxides under arbitrary incidence conditions is present to showcase the proof of concept.