<p>We study several notions of null sets on infinite-dimensional Carnot groups. We prove that a set is Aronszajn null if and only if it is null with respect to a certain class of measures that we call CAC measures. Such measures are non-abelian analogues of cube measures. As analogues of Gaussian measures we propose heat kernel measures as well as Gauss Haar measures, where the latter only makes sense when the commutator subgroup is locally compact. We show that groups with such a commutator subgroup have the structure of Banach manifolds. In this setting, we show that each set is Aronszajn null if and only if it is Gauss-Haar null. In the case of infinite-dimensional Heisenberg-like groups, we also show that being null in the previous senses is equivalent to being null for all heat kernel measures. This allows us to reformulate previously obtained Rademacher-type theorems in terms of these new null sets. Finally, we propose a number of open questions.</p>