Abstract Although active diapirs must deform the overburdens they pierce, the shape of passive (downbuilt or syn-depositional) diapirs is formed or molded by their overburdens. Molding of salt diapirs is simplified here to profiles of diapirs entirely downbuilt in effectively rigid overburden. The dips of salt-sediment contacts are shaped by the interaction of two processes: local net accumulation of overburden (A = deposition minus compaction) at rate A and the net increase in relief of salt structures (R = salt rise minus dissolution) at rate R. Steady kinematic molding ratios, R / A, forward model realistic dips of molded salt contacts, a, at particular depths using R / A or A / R = tan a/2. Rising or falling ratios of incremental molding forward model complete diapir profiles. Conversely, molding histories can be read by backstripping profiles of downbuilt diapirs. Salt diapirs are downbuilt in a field of downbuilding (100 > R / A > 0.01), that is bounded by burial and extrusion. Within this range, aggradation faster than salt can rise (R / A < 1) molds tapering (narrowing-upward) top contacts of salt. Accumulation of overburden slower than salt rises ( R / A > 1) molds flaring (widening-upward) salt contacts. Below this range (where R / A < -0.01), the top contact of the salt is eclipsed (temporarily buried to depths from which it can still upbuild) or even occluded (buried below its critical roof thickness and thus unable to rise again autonomously). Occluded salt is either dissolved at depth or rises in reactivated diapirs after exhumation or faulting of overburden that is not rigid. Where R / A > -100, salt emerges like a fountain and extrudes sheets of allochthonous salt. Extruded salt is recycled back into the ocean by dissolution at the surface or after burial and reactivation in another cycle.