The critical two-dimensional stochastic heat flow (2d SHF) is a two-parameter process of random Borel measures on R^4 derived in a breakthrough article by Caravenna, Sun, and Zygouras as a universal distributional limit of point-to-point partition functions for (1+2)-dimensional models of a directed polymer in a random environment within a critical weak-coupling scaling regime.  I will discuss continuum polymer measures associated with the 2d SHF, with an emphasis on the structure of their second moments. Our approach is inspired by a one-dimensional continuum directed polymer model formulated by Alberts, Khanin, and Quastel.