  Copy detection patterns (CDP) present an efficient technique for product
protection against counterfeiting. However, the complexity of studying CDP
production variability often results in time-consuming and costly procedures,
limiting CDP scalability. Recent advancements in computer modelling, notably
the concept of a "digital twin" for printing-imaging channels, allow for
enhanced scalability and the optimization of authentication systems. Yet, the
development of an accurate digital twin is far from trivial.
  This paper extends previous research which modelled a printing-imaging
channel using a machine learning-based digital twin for CDP. This model, built
upon an information-theoretic framework known as "Turbo", demonstrated superior
performance over traditional generative models such as CycleGAN and pix2pix.
However, the emerging field of Denoising Diffusion Probabilistic Models (DDPM)
presents a potential advancement in generative models due to its ability to
stochastically model the inherent randomness of the printing-imaging process,
and its impressive performance in image-to-image translation tasks.
  This study aims at comparing the capabilities of the Turbo framework and DDPM
on the same CDP datasets, with the goal of establishing the real-world benefits
of DDPM models for digital twin applications in CDP security. Furthermore, the
paper seeks to evaluate the generative potential of the studied models in the
context of mobile phone data acquisition. Despite the increased complexity of
DDPM methods when compared to traditional approaches, our study highlights
their advantages and explores their potential for future applications.
