ScoreSDEDataFidelity#

class deepinv.sampling.ScoreSDEDataFidelity(gamma=None, weight=1.0, rng=None, *args, **kwargs)[source]#

Bases: ALDDataFidelity

Score-SDE data-fidelity term.

This corresponds to the \(p(y|x_t)\) approximation proposed in [138], and reviewed in [35]. The difference with deepinv.sampling.ALDDataFidelity is that the measurements are noised to the current diffusion noise level before the mismatch is computed,

\[y_t = y + \sigma_t\epsilon, \qquad \epsilon\sim\mathcal{N}(0,\mathrm{Id}),\]

so that \(y_t\) and \(A x_t\) live at the same noise level. The resulting negative log-likelihood gradient is

\[-\nabla_{x_t} \log p_t(y|x_t) \approx \lambda \frac{A^\top \left(A x_t - y_t\right)}{\sigma_y^2 + \gamma_t^2},\]

where \(\lambda\), exposed as weight, controls the scale of the data-fidelity term.

Note

[35] writes this approximation without a guidance strength, noting that it then differs from deepinv.sampling.ALDDataFidelity only by the noising of the measurements. We keep the annealed guidance strength \(\sigma_y^2 + \gamma_t^2\) here, so that the term stays balanced against the unconditional score across noise levels.

Parameters:

  • gamma (Callable, float) – annealing parameter \(\gamma_t\). If None (default), \(\gamma_t = \sigma_t\), the current diffusion noise level.

  • weight (float) – Weighting factor \(\lambda\). Default: 1.0.

  • rng (torch.Generator) – Random number generator used to noise the measurements, for reproducibility. Default: None.

forward(*args, **kwargs)[source]#

Not implemented: the measurements are re-noised at every call, so this term has no deterministic value, see grad().

grad(x, y, physics, sigma, *args, **kwargs)[source]#

Compute the Score-SDE data-fidelity gradient \(\lambda A^\top \left(A x_t - y_t\right) / (\sigma_y^2 + \gamma_t^2)\).

Parameters:
Returns:

Score-SDE gradient, with the same shape as x.

Return type:

Tensor

Examples using ScoreSDEDataFidelity:#

Noisy data-fidelity terms for diffusion posterior sampling

Noisy data-fidelity terms for diffusion posterior sampling