It runs on the phone afaik, while speech recognition on the other hand is supported by stuff Google runs in the cloud.

Edit: I might be wrong, at the end of a paragraph they say it runs on Google’s TPU cloud infrastructure, though it isn't clear to me whether they just use that for training.

Edit 2: I just tried it on my phone. At least stuff like asking it to "Turn on WiFi" works without an internet connection, and yields a TTS response.

> I just tried it on my phone. At least stuff like asking it to "Turn on WiFi" works without an internet connection, and yields a TTS response.

But this is the status quo. You would not expect Google to disable offline TTS just for slightly improved quality. The real question is, is it running Wavenet offline or the previous version of its TTS engine offline?

Today's announcement is cloud-only. We also support an older algorithm for offline use that's less computationally intensive.

Is the offline one improving also? Google Maps often falls back to it (much more often than necessary for some reason) and it sounds completely different and far worse.

It runs in the cloud.

Google TTS supports both. Maps prefers the cloud one so that you're not at the mercy of whatever TTS your manufacturer has installed (Samsung uses their own, right?), but will fall back to the local one it there's no connectivity. I can't remember if the Google TTS implements that or if it's custom to Maps.