Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Sampling

Imagine you're trying to create a model that generates data by reversing a noisy process. You might think that if your model has low error in predicting the forward process, it will also perform well in generating data backward. However, this isn't always true. Sometimes, even with low errors, the model can behave unpredictably, leading to what’s called numerical instability. This can happen when the model's predictions diverge, meaning they don't converge to the expected results over time, which is a significant issue for anyone relying on these models for accurate outputs.

This paper addresses these issues by constructing a smooth score field that minimizes forward-marginal error while ensuring that the reverse-time process remains stable. The authors show that even when the forward errors are small, the model can still diverge in terms of its outputs. They introduce a family of denoisers that can help maintain accuracy and stability, even when the underlying processes are complex. This means that builders can create more reliable generative models that don't just look good on paper but also perform well in practice.

In practical terms, this work is crucial for anyone developing systems that rely on generative processes, as it provides a way to ensure that the models not only learn effectively but also produce stable and reliable outputs over time.

The paper introduces a new perspective on score matching and numerical stability in reverse-time processes.

The claims are supported by experiments with a specific network, though broader validation could enhance reliability.