  We present experimental tests of dissipative extensions of spontaneous wave
function collapse models based on a levitated micromagnet with ultralow
dissipation. The spherical micromagnet, with radius $R=27$ $\mu$m, is levitated
by Meissner effect in a lead trap at $4.2$ K and its motion is detected by a
SQUID. We perform accurate ringdown measurements on the vertical translational
mode with frequency $57$ Hz, and infer the residual damping at vanishing
pressure $\gamma/2\pi<9$ $\mu$Hz. From this upper limit we derive improved
bounds on the dissipative versions of the CSL (continuous spontaneous
localization) and the DP (Di\'{o}si-Penrose) models with proper choices of the
reference mass. In particular, dissipative models give rise to an intrinsic
damping of an isolated system with the effect parameterized by a temperature
constant; the dissipative CSL model with temperatures below 1 nK is ruled out,
while the dissipative DP model is excluded for temperatures below $10^{-13}$ K.
Furthermore, we present the first bounds on dissipative effects in a more
recent model, which relates the wave function collapse to fluctuations of a
generalized complex-valued spacetime metric.
