Configuration space is a critical but perhaps generally underappreciated element of standard quantum mechanics, in most of its various formulations (e.g., in the Hilbert space formulation). It is the space defined by the multiparticle configuration of all the elements of relevance to a given experimental setup being analyzed.
Because it describes the configuration of these elements, it is exponential in size, with a different space corresponding to each combination of such elements, and manifestly non-local. Thus, it is an entirely implausible, highly problematic element of standard quantum mechanical approaches, including the existing pilot-wave models.
The need for configuration space at a mathematically deep level arises because the equations being used are linear, so they cannot represent any kind of actual interaction among different particles. Without configuration space, every particle would fully superpose on every other particle — they would just slip on past each other. This is in fact how bosons (e.g., photons) behave, but not how fermions like electrons behave.
The pilot-wave approach has been (perhaps unfairly) criticized for using configuration space, because it posits that the wave function is actually a “real” thing, thus exposing the implausibility of this otherwise purely calculational tool. See Norsen et al., 2015 for an analysis of the contributions of configuration space to the pilot-wave results. They concluded that indeed the configuration space contains a large amount of “redundant” information, and that even the simplest approximation for the inter-particle interaction terms does a reasonable (yet imperfect) job of capturing the behavior of the full configuration-space model. Exploration of higher-order terms in this approximation are ongoing (Norsen, 2022).
If the underlying dynamics of the system are nonlinear, and in particular involve interactions between stochastic particles and wave functions, then it is possible that these nonlinear interactions end up producing all of the relevant dynamics that are otherwise captured via the configuration space calculational tool. This is the approach taken here.