A Practical Diffusion Path for Sampling
<|reference_start|>A Practical Diffusion Path for Sampling: Diffusion models are state-of-the-art methods in generative modeling when samples from a target probability distribution are available, and can be efficiently sampled, using score matching to estimate score vectors guiding a Langevin process. However, in the setting where samples from the target are not available, e.g. when this target's density is known up to a normalization constant, the score estimation task is challenging. Previous approaches rely on Monte Carlo estimators that are either computationally heavy to implement or sample-inefficient. In this work, we propose a computationally attractive alternative, relying on the so-called dilation path, that yields score vectors that are available in closed-form. This path interpolates between a Dirac and the target distribution using a convolution. We propose a simple implementation of Langevin dynamics guided by the dilation path, using adaptive step-sizes. We illustrate the results of our sampling method on a range of tasks, and shows it performs better than classical alternatives.<|reference_end|>
@article{chehab2024a,
    title={A Practical Diffusion Path for Sampling},
    author={Omar Chehab, Anna Korba},
    journal={arXiv preprint arXiv:2406.14040},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.14040},
    primaryClass={stat.ML cs.LG}
}