Collapsing is a post-quantum strengthening of collision resistance, needed to lift many classical results to the quantum setting. Unfortunately, the only existing standard-model proofs of collapsing hashes require LWE. We construct the first collapsing hashes from the quantum hardness of any one of the following problems: LPN in a variety of low noise or high-hardness regimes, essentially matching what is known for collision resistance from LPN.Finding cycles on exponentially-large expander graphs, such as those arising from isogenies on elliptic curves.The “optimal” hardness of finding collisions in any hash function.The polynomial hardness of finding collisions, assuming a certain plausible regularity condition on the hash. As an immediate corollary, we obtain the first statistically hiding post-quantum commitments and post-quantum succinct arguments (of knowledge) under the same assumptions. Our results are obtained by a general theorem which shows how to construct a collapsing hash H′ from a post-quantum collision-resistant hash function H, regardless of whether or not H itself is collapsing, assuming H satisfies a certain regularity condition we call “semi-regularity”.