The nonlocal version of de Broglie pilot waves is distinct from Bohm's nonlocal hidden variables theory
I see that there is a lot of fascinating and often well-thought posts about "Bohm-de Broglie" interpretation of quantum physics, including such phrases as "Bohm-de Broglie pilot wave theory." Now there have been very intense thinking by physicists and non-physicists alike over the past 75 years since de Broglie, then Bohm, launched alternative interpretations of the available quantum empirical data. As most have noticed, the 'orthodox' interpretation by Niels Bohr and his nearest companions held a view that did not invite enquiry into such all-important concepts as "nonlocality", which was first made explicit by works many decades later, notably by J.S. Bell.
One of the features of de Broglie's pilot wave interpretation was that he regarded as photon as a particle with near-zero mass (instead of zero mass), guided by a pilot wave. He did not in the first version include the concept of nonlocality, which didn't quite exist at the time (although 'locality' did exist in the socalled EPR paper). His theory did not work out correctly, therefore, in terms of numerical implications.
When David Bohm launched his hidden variable theory, he had not heard about this alternative interpretation by de Broglie. Bohm's quantum potential was nonlocal and a different wave type than the socalled pilot waves of de Broglie. Bohm's theory had however the important virtue of yielding the same numerical predictions as conventional quantum theory. At first, there were no empirical advantages to this, but there was a possibility that one could re-ignite worldview assumption thinking through this interpretation and that is indeed what happened.
Later on, de Broglie read Bohm's theory and published, in his 1950s book, his thoughts on these. In short, he disagreed with Bohm's quantum potential idea, but agreed to the nonlocality idea, and applied it to his pilot waves and got the correct predictions. There are therefore two branches here of the nonlocal interpretations of quantum theories from the 1950s--that of bohmian mechanics, and that of the nonlocal de Broglie pilot wave interpretation. The latter has adherents in the form of active physicists working on it well aware of these distinctions.
Many other interpretations have been launched of the quantum data since then, often so as to try to incorporate some parts of Einstein's predictions on gravitation, and/or his assumptions, but most of these interpretations are leaning heavily on works by David Bohm and by Louis de Broglie in their ideas of nonlocality. In my own works, summarized in what I call 'Super-Model Theory', I give an algorithmic rather than mathematical summary in which a leading assumption is that nonlocality as according eg to Louis de Broglie must be regarded as more fundamental than that which Albert Einstein proposed as for the constancy of speed of light.
