Inferring for non-exponential family models

Say I have a non exponential Bayesian model which is constructed with tensor flow operation such as tf.cumsum, tf.where etc.
Can I still expect Edward to offer automatic inference or am I obliged to provide the posterior distribution (compute it analytically). According to the documentation the necessary conditions for complete_conditional are:

  1. tractable exponential family; and
  2. the truth of assumption 1 is not obscured in the TensorFlow graph

Are there any solver which can work without these assumptions?