Min-SNR Weights for v-Prediction

mediumPROSignal-to-Noise Ratio and Loss WeightingDiffusion ModelsDiffusion Models 1

Problem Statement

Min-SNR weighting changes form with the prediction target. For v-prediction the effective weight uses SNR + 1 in the denominator. Compute it.

Background

Hang et al. give the Min-SNR weight per parameterization by dividing the clamped SNR by the parameterization's implicit weight:

eps-pred: w = min(SNR, gamma) / SNR
x0-pred: w = min(SNR, gamma)
v-pred: w = min(SNR, gamma) / (SNR + 1)

The SNR + 1 denominator for v reflects that v-prediction already balances signal and noise, so its baseline weight is SNR + 1.

Your Task

Implement:

def min_snr_v_weights(snr, gamma):

Return the list of v-prediction Min-SNR weights rounded to 4 decimals.

Input Format

snr: list of non-negative SNRs.
gamma (float): the clamp.

Output Format

A list of floats rounded to 4 decimals.

Sample

print(min_snr_v_weights([10.0, 4.0, 1.0], 5.0))

Output:

[0.4545, 0.8, 0.5]

Example

Input

print(min_snr_v_weights([10.0, 4.0, 1.0], 5.0))

Output

[0.4545, 0.8, 0.5]

Reasoning

For each SNR value, the weight is calculated using the v-prediction formula: $w = \frac{\min(\text{SNR}, \gamma)}{\text{SNR} + 1}$ . The numerator clamps the SNR to the maximum value $\gamma$ to prevent weights from becoming too large, while the denominator accounts for the signal-to-noise ratio plus one, specific to v-prediction.
For the first input $\text{SNR} = 10.0$ with $\gamma = 5.0$ , the numerator is $\min(10.0, 5.0) = 5.0$ and the denominator is $10.0 + 1 = 11.0$ . The weight is $5.0 / 11.0 \approx 0.454545$ , which rounds to $0.4545$ .
For the second input $\text{SNR} = 4.0$ with $\gamma = 5.0$ , the numerator is $\min(4.0, 5.0) = 4.0$ and the denominator is $4.0 + 1 = 5.0$ . The weight is $4.0 / 5.0 = 0.8$ , which remains $0.8$ when rounded to 4 decimals.
For the third input $\text{SNR} = 1.0$ with $\gamma = 5.0$ , the numerator is $\min(1.0, 5.0) = 1.0$ and the denominator is $1.0 + 1 = 2.0$ . The weight is $1.0 / 2.0 = 0.5$ , which remains $0.5$ when rounded to 4 decimals.
The final output is [0.4545, 0.8, 0.5]

Constraints

1 <= len(snr) <= 100000, all snr[i] >= 0, gamma > 0.
w_t = min(SNR_t, gamma) / (SNR_t + 1).
Round to 4 decimals.

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1. Background Knowledge

In diffusion models, the training loss is often weighted by a function of the signal-to-noise ratio (SNR) to balance the contribution of different noise levels. The Min-SNR weighting scheme, introduced by Hang et al., addresses the issue that standard weighting can under- or over-emphasize certain timesteps. The core idea is to clamp the SNR at a threshold $\gamma$ to prevent extreme weights.

The form of the weight depends on the prediction target (parameterization). For $\epsilon$ -prediction, the model predicts noise, and the implicit weight is proportional to $1/\text{SNR}$ . For $x_0$ -prediction, the model predicts the clean signal, and the implicit weight is proportional to $1$ . For v-prediction, the model predicts a velocity-like quantity that is a linear combination of the signal and noise. This parameterization inherently balances both components, leading to an implicit weight proportional to $1/(\text{SNR} + 1)$ .

The Min-SNR weight for a given parameterization is defined as the clamped SNR divided by the parameterization's implicit weight. For v-prediction, this results in the formula:

w = \frac{\min(\text{SNR}, \gamma)}{\text{SNR} + 1}

This ensures that for high SNR values (low noise), the weight is capped by $\gamma / (\text{SNR} + 1)$ , while for low SNR values (high noise), the weight is $\text{SNR} / (\text{SNR} + 1)$ , which approaches 1 as SNR becomes large but is small when SNR is near zero.

2. Algorithm Approach

The problem requires applying a vectorized mathematical operation to a list of SNR values. The approach involves:

Iterating through each SNR value in the input list.
Computing the clamped SNR: $\text{clamped\_snr} = \min(\text{snr}_i, \gamma)$ .
Computing the denominator: $\text{denom} = \text{snr}_i + 1$ .
Calculating the weight: $w_i = \text{clamped\_snr} / \text{denom}$ .
Rounding the result to 4 decimal places.
Collecting all weights into a list.

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