A non-volatile storage system includes a memory controller connected to an integrated memory assembly. The integrated memory assembly includes a memory die comprising non-volatile memory cells and a control die bonded to the memory die. The memory controller provides data to the control die for storage on the memory die. Data is initially stored on the memory die as single bit per memory cell data to increase the performance of the programming process. Subsequently, the control die performs an adaptive folding process which comprises reading the single bit per memory cell data from the memory die, adaptively performing one of multiple decoding options, and programming the data back to the memory die as multiple bit per memory cell data.