Propagation Is Not Decoration: When Physical Diffraction Carries Generative Computation
Abstract
We introduce the conditioned Diffraction Field Model (cDFM), a generative architecture built from Wave-Aperture-Diffraction (WAD) blocks. Each block conditions a complex field with a learned, class-conditioned aperture and propagates it with a fixed Angular Spectrum Method (ASM) operator. One random field is carried through four resolutions and read out directly as intensity, with no learned decoder. A learned aperture can form images by itself and bypass propagation, so the presence of propagation in such a model does not show that it does any work. We test this by retraining eight controls from scratch with matched parameter counts and update budgets. In an earlier image-fitting model, restricting the aperture to 16x16 spatial resolution lets ASM remove 30.7% of the excess error of a retrained bypass, compared with 2.1% at 64x64. On MNIST, the full generator reaches 83.1% class accuracy from fresh sources across three seeds. Replacing ASM with the identity, E(x)=x, drops this to 20.3%, and rebuilding the source at each scale drops it to 16.4%. An identity control whose aperture can amplify light reaches 78.5%, so the identity drop depends on the aperture being passive, as a physical aperture is. A nonphysical operator matched to ASM's local reach reaches 77.0%, and a global permuted spectral operator 55.7%. A wider version (994k parameters) trained for 30 epochs reaches 95.9% on one seed. Retrained at that budget, the passive identity control reaches 90.3% and the permuted spectral control 94.1%, but both fit held-out digits worse. In a separate strict-locality task, identity evolution leaves distant prediction at chance (25%), ASM at propagation distance 20 reaches 55%, and a global random unitary and a permuted spectral operator reach 86% and 88%. Propagation matters most in this generator when the aperture is passive and the learned path is small or briefly trained, and less as the learned path grows. In the locality task, diffraction is one of several global operators that can carry distant information. On CIFAR-10 the same design produced mostly blobs with a coarse lattice texture, so the generative results are limited to MNIST.
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