  The bipolar filtration of Cochran, Harvey and Horn presents a framework of
the study of deeper structures in the smooth concordance group of topologically
slice knots. We show that the graded quotient of the bipolar filtration of
topologically slice knots has infinite rank at each stage greater than one. To
detect nontrivial elements in the quotient, the proof simultaneously uses
higher order amenable Cheeger-Gromov $L^2$ $\rho$-invariants and infinitely
many Heegaard Floer correction term $d$-invariants.
