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Guidance Rescaling to Fix Over-Exposure

MediumDiffusion Models 📚 Diffusion Models 1

Problem Statement

High CFG scales inflate the predicted-noise magnitude, over-exposing images. Lin et al.'s guidance rescale trick renormalizes the guided prediction back toward the conditional prediction's standard deviation. Implement it.

Background

Let eps_cfg be the guided prediction and eps_cond the plain conditional one. Compute their standard deviations (over all elements, population std), rescale the guided prediction to the conditional's std, then blend by a factor phi:

$\varepsilon_{\text{rescaled}} = \varepsilon_{\text{cfg}} \cdot \frac{\text{std}(\varepsilon_{\text{cond}})}{\text{std}(\varepsilon_{\text{cfg}})}, \qquad \varepsilon_{\text{final}} = \phi\,\varepsilon_{\text{rescaled}} + (1 - \phi)\,\varepsilon_{\text{cfg}}$

phi = 0 disables the fix; phi = 1 fully rescales. If std(eps_cfg) is 0, skip the rescale (return eps_cfg).

Your Task

Implement:

def guidance_rescale(eps_cfg, eps_cond, phi):

Return the final prediction as a list rounded to 4 decimals.

Input Format

eps_cfg, eps_cond: lists of equal length D.
phi (float) in [0, 1].

Output Format

A list of D floats rounded to 4 decimals.

Sample

print(guidance_rescale([2.0, -2.0], [1.0, -1.0], 1.0))

Output:

[1.0, -1.0]

Example:

Input:

print(guidance_rescale([2.0, -2.0], [1.0, -1.0], 1.0))

Output:

[1.0, -1.0]

Reasoning:

Compute the population standard deviation of the guided prediction eps_cfg = [2.0, -2.0]. The mean is $0$ , so $\text{std}(\varepsilon_{\text{cfg}}) = \sqrt{\frac{(2.0)^2 + (-2.0)^2}{2}} = \sqrt{4} = 2.0$ .
Compute the population standard deviation of the conditional prediction eps_cond = [1.0, -1.0]. The mean is $0$ , so $\text{std}(\varepsilon_{\text{cond}}) = \sqrt{\frac{(1.0)^2 + (-1.0)^2}{2}} = \sqrt{1} = 1.0$ .
Since $\text{std}(\varepsilon_{\text{cfg}}) \neq 0$ , calculate the rescaled prediction by scaling eps_cfg by the ratio of the standard deviations: $\varepsilon_{\text{rescaled}} = [2.0, -2.0] \cdot \frac{1.0}{2.0} = [1.0, -1.0]$ .
Blend the rescaled prediction with the original guided prediction using $\phi = 1.0$ . This fully applies the rescaling: $\varepsilon_{\text{final}} = 1.0 \cdot [1.0, -1.0] + (1 - 1.0) \cdot [2.0, -2.0] = [1.0, -1.0]$ .
The final output is [1.0, -1.0]

Constraints:

len(eps_cfg) == len(eps_cond), 0 <= phi <= 1.
Use population std (ddof=0) over all elements.
If std(eps_cfg) == 0, return eps_cfg unchanged.
Round to 4 decimals; avoid -0.0.

More from Diffusion Models 1

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1. Background Knowledge

In classifier-free guidance (CFG), the model makes two noise predictions per step: an unconditional one $\varepsilon_{\text{uncond}}$ and a conditional one $\varepsilon_{\text{cond}}$ . The guided prediction is formed as $\varepsilon_{\text{cfg}} = \varepsilon_{\text{uncond}} + w\,(\varepsilon_{\text{cond}} - \varepsilon_{\text{uncond}})$ , where $w$ is the guidance scale. As $w$ grows, the magnitude of $\varepsilon_{\text{cfg}}$ inflates, which in latent space translates to over-exposed or saturated images.

The guidance rescale trick (Lin et al.) observes that the direction of the guided prediction is useful, but its scale is not. By renormalizing $\varepsilon_{\text{cfg}}$ so that its standard deviation matches that of $\varepsilon_{\text{cond}}$ , you keep the guidance direction while restoring a sane noise magnitude. A blending factor $\phi \in [0,1]$ lets you interpolate between the raw guided prediction ( $\phi=0$ ) and the fully rescaled one ( $\phi=1$ ).

The standard deviation used here is the population standard deviation (divide by $N$ , not $N-1$ ), computed over all elements of the vector. This is a simple element-wise scaling operation followed by a convex combination.

2. Algorithm Approach

This is a vector normalization and blending problem. The core pattern is:

Compute a scalar statistic (std) from each input vector.
Use the ratio of the two scalars as a multiplicative scale factor.
Apply the scale to one vector, then take a weighted average with the original.

No loops over dimensions are needed beyond the final element-wise operations. The entire computation reduces to a handful of scalar arithmetic steps plus one pass over the vectors for the std calculations and the final blend.

3. Step-by-Step Strategy

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solution.py

Python 3.13

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