Conditional generative models are capable of using contextual information as input to create new imaginative outputs. Conditional Restricted Boltzmann Machines (CRBMs) are one class of conditional generative models that have proven to be especially adept at modeling noisy discrete or continuous data, but the lack of expressivity in CRBMs have limited their widespread adoption. Here we introduce Neural Boltzmann Machines (NBMs) which generalize CRBMs by converting each of the CRBM parameters to their own neural networks that are allowed to be functions of the conditional inputs. NBMs are highly flexible conditional generative models that can be trained via stochastic gradient descent to approximately maximize the log-likelihood of the data. We demonstrate the utility of NBMs especially with normally distributed data which has historically caused problems for Gaussian-Bernoulli CRBMs. Code to reproduce our results can be found at https://github.com/unlearnai/neural-boltzmann-machines.