Stable Target Field for Reduced Variance Score Estimation in Diffusion Models

TL;DR

This paper identifies large target variance in diffusion-model score learning, particularly in an intermediate forward-time regime where multiple data modes influence the score. It introduces Stable Target Field (STF), which uses a large reference batch with self-normalized importance weights to produce stabilized targets for denoising score-matching. The authors prove that STF is asymptotically unbiased and reduces the training-target covariance by a factor ~1/(n−1) under mild conditions, while introducing a bias that vanishes as the reference batch grows. Empirically, STF improves image quality, stability, and training speed across VE, VP, and EDM, achieving state-of-the-art CIFAR-10 generation (FID 1.90 with 35 NFEs using EDM) and offering noticeable speedups, thereby making diffusion-model training more efficient and robust.

Abstract

Diffusion models generate samples by reversing a fixed forward diffusion process. Despite already providing impressive empirical results, these diffusion models algorithms can be further improved by reducing the variance of the training targets in their denoising score-matching objective. We argue that the source of such variance lies in the handling of intermediate noise-variance scales, where multiple modes in the data affect the direction of reverse paths. We propose to remedy the problem by incorporating a reference batch which we use to calculate weighted conditional scores as more stable training targets. We show that the procedure indeed helps in the challenging intermediate regime by reducing (the trace of) the covariance of training targets. The new stable targets can be seen as trading bias for reduced variance, where the bias vanishes with increasing reference batch size. Empirically, we show that the new objective improves the image quality, stability, and training speed of various popular diffusion models across datasets with both general ODE and SDE solvers. When used in combination with EDM, our method yields a current SOTA FID of 1.90 with 35 network evaluations on the unconditional CIFAR-10 generation task. The code is available at https://github.com/Newbeeer/stf

Figures (10)

• Figure 1: Illustration of differences between the DSM objective and our proposed STF objective. The "destroyed" images (in blue box) are close to each other while their sources (in red box) are not. Although the true score in expectation is the weighted average of ${\mathbf{v}}_i$, the individual training updates of the DSM objective have a high variance, which our STF objective reduces significantly by including a large reference batch (yellow box).
• Figure 2: (a): Illustration of the three phases in a two-mode distribution. (b): Estimated $V_\textrm{DSM}(t)$ for two distributions. We normalize the maximum value to 1 for illustration purposes.
• Figure 2: FID and NFE on CelebA $64^2$
• Figure 3: (a, b): $V_\textrm{DSM}(t)$ and $D(t)$ versus $t$. We normalize the maximum values to $1$ for illustration purposes. (c, d): $V_{\textrm{STF}}(t)$ with a varying reference batch size $n$.
• Figure 4: FID and generated samples throughout training on (a) CIFAR-10 and (b) CelebA $64^2$.

Theorems & Definitions (6)

• Theorem 1
• Theorem 2
• Theorem 2
• proof
• Theorem 2
• proof