Guidance Rescaling to Fix Over-Exposure

mediumPROGuidance and Latent DiffusionDiffusion ModelsDiffusion 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.

Learn this in

Sampling & AccelerationDiffusion Study Plan Conditional GenerationDiffusion Study Plan

More from Diffusion Models 1

Classifier-Free Guidance: Uncond/Cond Mixingeasy DDPM Posterior Mean and Variance from x0medium Adaptive CFG Scheduling over the Trajectoryhard Classifier Gradient Guidance Stepmedium Negative Prompt as the Unconditional Branchmedium

Concept primerPREVIEW

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

PRO

Continue the full explanation

You're reading the free preview. Unlock the complete walkthrough, the code editor, test runner and reference solution with Premium.

PRO

Editor locked

The code editor is locked for Pro problems. It is only available for free problems. Please upgrade to gain access to the code editor for all problems.

solution.py

Python 3.13

Test results