class

NCSNForImageGeneration

extendsPretrainedModel

NCSNForImageGeneration(config: NCSNConfig)

source edit

NCSN with the DSM training loss and annealed Langevin .generate().

Wraps NCSNModel with denoising score matching (DSM) for training and annealed Langevin dynamics for inference. Sampling does not reuse DiffusionMixin.generate because NCSN's nested (per- $\sigma$ x per-step) loop has different semantics from the DDPM scheduler step.

Training contract forward(x) samples a random noise-level index per image, perturbs x accordingly, runs the score network, and returns the DSM loss (Song 2019 Eq. 6).

Sampling generate(n_samples) runs annealed Langevin dynamics across the full $\sigma$ schedule (Song 2019 Algorithm 1).

Parameters

configNCSNConfig

Hyperparameters controlling architecture, noise schedule, and Langevin sampler.

Attributes

ncsnNCSNModel

Underlying score network (see NCSNModel).

sigmasTensor

Buffer of shape (num_noise_levels,) holding the geometric

\sigma

schedule (mirrored from self.ncsn.sigmas for convenience in loss / sampling code).

Notes

Reference: Song and Ermon, "Generative Modeling by Estimating Gradients of the Data Distribution", NeurIPS, 2019 (arXiv:1907.05600); NCSNv2 refinements in Song and Ermon, 2020 (arXiv:2006.09011).

Denoising score matching loss:

\mathcal{L}_{\text{DSM}}(\theta) = \tfrac{1}{2}\, \mathbb{E}_{\sigma, x, \tilde{x}}\!\left[ \big\lVert \sigma\, s_\theta(\tilde{x}, \sigma) + z \big\rVert^2 \right],

with $\tilde{x} = x + \sigma z$ , $z \sim \mathcal{N}(0, \mathbf{I})$ .

Examples

>>> import lucid
>>> from lucid.models.generative.ncsn import (
...     NCSNConfig, NCSNForImageGeneration,
... )
>>> cfg = NCSNConfig(sample_size=32, base_channels=32,
...                  channel_mult=(1, 2), num_res_blocks=1,
...                  resnet_groups=16, num_noise_levels=10,
...                  langevin_steps=2)
>>> model = NCSNForImageGeneration(cfg).eval()
>>> x = lucid.randn((1, 3, 32, 32))
>>> out = model(x)
>>> out.sample.shape, out.loss.shape   # score field + scalar loss
((1, 3, 32, 32), ())

Used by 2

Constructors

dunder

init

→None

__init__(config: NCSNConfig)

source edit

Instance methods

forward

→DiffusionModelOutput

forward(sample: Tensor)

source edit

Denoising Score Matching loss (Song 2019 Eq. 6).

For each image we sample i ~ Uniform({0, …, L-1}), perturb x̃ = x + σ_i · z with z ~ N(0, I), and minimise

L = ½ · E ‖ σ_i · s_θ(x̃, i) + z ‖²

which is the σ-weighted DSM loss.

generate

→GenerationOutput

generate(n_samples: int = 1, langevin_steps: int | None = None, return_intermediates: bool = False, device: str = 'cpu')

source edit

Annealed Langevin dynamics — Song 2019 Algorithm 1.

Initialises x ~ N(0, σ_max² I) then iterates over the σ schedule from largest to smallest noise. At each σ_i takes langevin_steps Langevin steps with step size α_i = ε · σ_i² / σ_L²:

x ← x + (α_i / 2) · s_θ(x, i) + √α_i · z z ~ N(0, I)

Parameters

n_samplesint= 1

Batch size of the generated images.

langevin_stepsint | None= None

Override config.langevin_steps for this call (typically lowered in unit tests).

return_intermediatesbool= False

If True, also returns one sample per σ level (after its inner Langevin loop).

devicestr= 'cpu'

Where to allocate the initial noise.

Returns

GenerationOutput

class:GenerationOutput with the final (n_samples, C, H, W)

>>> import lucid >>> from lucid.models.generative.ncsn import ( ... NCSNConfig, NCSNForImageGeneration, ... ) >>> cfg = NCSNConfig(sample_size=32, base_channels=32, ... channel_mult=(1, 2), num_res_blocks=1, ... resnet_groups=16, num_noise_levels=10, ... langevin_steps=2) >>> model = NCSNForImageGeneration(cfg).eval() >>> x = lucid.randn((1, 3, 32, 32)) >>> out = model(x) >>> out.sample.shape, out.loss.shape # score field + scalar loss ((1, 3, 32, 32), ())

generate

→GenerationOutput

generate(n_samples: int = 1, langevin_steps: int | None = None, return_intermediates: bool = False, device: str = 'cpu')

source edit

Annealed Langevin dynamics — Song 2019 Algorithm 1.

Initialises x ~ N(0, σ_max² I) then iterates over the σ schedule from largest to smallest noise. At each σ_i takes langevin_steps Langevin steps with step size α_i = ε · σ_i² / σ_L²:

x ← x + (α_i / 2) · s_θ(x, i) + √α_i · z z ~ N(0, I)

Parameters

n_samplesint= 1

Batch size of the generated images.

langevin_stepsint | None= None

Override config.langevin_steps for this call (typically lowered in unit tests).

return_intermediatesbool= False

If True, also returns one sample per σ level (after its inner Langevin loop).

devicestr= 'cpu'

Where to allocate the initial noise.

Returns

GenerationOutput

class:GenerationOutput with the final (n_samples, C, H, W)