An Unconditional Representation of the Conditional Score in Infinite-Dimensional Linear Inverse Problems

arXiv — stat.MLTuesday, November 25, 2025 at 5:00:00 AM
  • A novel approach to linear inverse problems has been introduced through an unconditional representation of the conditional score function (UCoS), which significantly reduces computational costs by eliminating the need for multiple forward model evaluations during sampling. This method leverages an offline training phase to learn a task-dependent score function based on the linear forward operator.
  • The development of UCoS is crucial for enhancing the efficiency of Bayesian inverse problems, particularly in applications such as high-dimensional computed tomography and image deblurring, where traditional methods can be computationally prohibitive.
  • This advancement reflects a broader trend in machine learning towards improving sampling efficiency and accuracy, addressing challenges such as the blindness problem in score matching and the need for better data assimilation techniques in generative models, which are essential for various applications in artificial intelligence.
— via World Pulse Now AI Editorial System

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