Forward-only Diffusion Probabilistic Models

This work presents a forward-only diffusion (FoD) approach for generative modelling. In contrast to traditional diffusion models that rely on a coupled forward-backward diffusion scheme, FoD directly learns data generation through a single forward diffusion process, yielding a simple yet efficient generative framework. The core of FoD is a state-dependent linear stochastic differential equation that involves a mean-reverting term in both the drift and diffusion functions. This mean-reversion property guarantees the convergence to clean data, naturally simulating a stochastic interpolation between source and target distributions. More importantly, FoD is analytically tractable and is trained using a simple stochastic flow matching objective, enabling a few-step non-Markov chain sampling during inference. The proposed FoD model, despite its simplicity, achieves competitive performance on various image-conditioned (e.g., image restoration) and unconditional generation tasks, demonstrating its effectiveness in generative modelling. Our code is available atthis https URL.

@article{luo2025_2505.16733,
  title={ Forward-only Diffusion Probabilistic Models },
  author={ Ziwei Luo and Fredrik K. Gustafsson and Jens Sjölund and Thomas B. Schön },
  journal={arXiv preprint arXiv:2505.16733},
  year={ 2025 }
}