As noticed by @parras @pfrank and me the adjoint of the linearization of the correlated field model is very slow if total_N != 0. Here is a demo: ``` import nifty8 as ift import numpy as np sp1 = ift.RGSpace((4000, 4000)) cfmaker = ift.CorrelatedFieldMaker('') cfmaker.add_fluctuations(sp1, (0.1, 1e-2), (2, .2), (.01, .5), (-4, 2.), 'amp1') cfmaker.set_amplitude_total_offset(0., (1e-2, 1e-6)) cf0 = cfmaker.finalize(0) n_tot=1 cfmaker = ift.CorrelatedFieldMaker('', total_N=n_tot) cfmaker.add_fluctuations(sp1, (0.1, 1e-2), (2, .2), (.01, .5), (-4, 2.), 'amp1', dofdex=np.arange(n_tot)) cfmaker.set_amplitude_total_offset(0., (1e-2, 1e-6), dofdex=np.arange(n_tot)) cf1 = cfmaker.finalize(0) print("benchmark for total_N = 0") ift.exec_time(cf0) print("benchmark for total_N = 1") ift.exec_time(cf1) ``` I had a quick look at the issue. The problem seems to be the _Distributor operator in the correlated field model file: https://gitlab.mpcdf.mpg.de/ift/nifty/-/blob/NIFTy_8/src/library/correlated_fields.py#L214 For the case of total_N != 0 this _Distributor is called multiple times. The call which is very slow in adjoint direction is in line: https://gitlab.mpcdf.mpg.de/ift/nifty/-/blob/NIFTy_8/src/library/correlated_fields.py#L362 and the line below. Note this _Distibutor operator is only used for the case total_N != 0, and therefore the simple case with total_N = 0 is reasonably fast.