The category of Soergel bimodules is a well-behaved categorification of the Hecke algebra of a Coxeter group. In many characteristic 0 realizations, the indecomposable objects in this category correspond to the Kazhdan-Lusztig basis, thereby giving an explanation for the positivity of Kazhdan-Lusztig polynomials. In characteristic $p>0$ the indecomposable objects give rise to another set of non-negative Laurent polynomials called $p$-Kazhdan-Lusztig polynomials, which can be used as a replacement for Kazhdan-Lusztig polynomials in modular representation theory. In this talk I will propose a non-negative replacement for inverse Kazhdan-Lusztig polynomials in positive characteristic.