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Classifier-Free Guidance

Diffusion ModelsSamplingConditional Generation

Medium

Combine a conditional and an unconditional model prediction with classifier-free guidance, optionally rescaling the result per sample.

g = u + w\,(c - u)

Here $c$ is cond_pred, $u$ is uncond_pred, both of shape (B, ...), and $w$ is guidance_scale. When guidance_rescale $\phi$ is 0, return $g$ .

When $\phi > 0$ , compute for every sample $b$ the population standard deviation (dividing by the number of elements, with no Bessel correction) over all of its non-batch elements, written $s(\cdot)$ , and blend

r_b = g_b \, \frac{s(c_b)}{s(g_b)}, \qquad \text{result}_b = \phi\, r_b + (1 - \phi)\, g_b .

Each sample uses its own two standard deviations. The value $\phi = 1$ returns the fully rescaled prediction.

Return a PyTorch tensor with the same shape, dtype and device as cond_pred.

Examples

Input: cond_pred = [[[[0.6,-0.2],[1.0,0.4]]],[[[0.1,0.3],[-0.5,0.2]]]], uncond_pred = [[[[0.4,0.0],[0.5,0.3]]],[[[0.2,0.1],[-0.1,0.0]]]], guidance_scale = 3.0, guidance_rescale = 0.0

Output: [[[[1.0,-0.6],[2.0,0.6]]],[[[-0.1,0.7],[-1.3,0.6]]]]

Explanation: With guidance_scale = 3 each value moves three times the gap away from the unconditional prediction, so the first pixel becomes 0.4 + 3 (0.6 - 0.4) = 1.0. A rescale of 0 leaves this guided result unchanged.

Input: cond_pred = [[[[0.6,-0.2],[1.0,0.4]]],[[[0.1,0.3],[-0.5,0.2]]]], uncond_pred = [[[[0.4,0.0],[0.5,0.3]]],[[[0.2,0.1],[-0.1,0.0]]]], guidance_scale = 3.0, guidance_rescale = 1.0

Output: [[[[0.464907,-0.278944],[0.929814,0.278944]]],[[[-0.039001,0.273009],[-0.507017,0.234008]]]]

Input: cond_pred = [[1.0,2.0,0.0,-1.0],[0.5,-0.5,0.5,-0.5]], uncond_pred = [[0.5,1.0,0.5,0.0],[0.0,0.0,0.0,0.0]], guidance_scale = 7.5, guidance_rescale = 0.7

Output: [[1.807397,3.614794,-1.382127,-3.189524],[1.475,-1.475,1.475,-1.475]]

Hint 1

tuple(range(1, g.ndim)) lists every non-batch dimension for any input rank.

Hint 2

g.std(dim=dims, keepdim=True, correction=0) gives a population std per sample; the default divides by n - 1 and will not match.

Hint 3

keepdim=True keeps a (B, 1, ...) shape that broadcasts back over the sample.

Requirements

Use PyTorch tensor operations.
Leave all input tensors unchanged.

Constraints

cond_pred and uncond_pred are floating-point PyTorch tensors of the same shape (B, ...) with B at least 1 and at least two elements per sample.
guidance_scale is a Python float, usually between 1 and 12, and it may be 0 or negative.
guidance_rescale is a Python float in [0, 1].
Whenever guidance_rescale is above 0, every sample of the guided prediction has a standard deviation above 0.
Supported dtypes are float32 and float64. All values are finite.

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