Both Kaldi[1] and CMU Sphinx[2] are high-quality open source speech systems. I know for a fact that Kaldi includes support for DNN acoustic models (I'm less familiar with Sphinx).

[1] http://kaldi.sourceforge.net/ [2] http://cmusphinx.sourceforge.net/

Thanks, appreciated, but my dear lord, without a PhD in AI systems these things are a bit beyond what most users, me included, would casually play around with. Be great if this tech made it into Dragon Naturally Speaking-like end product to use privately.