Diffusion and Auxiliary Losses

DepthDif always computes a base diffusion loss. Optional auxiliary terms can add sparse-anchor, profile-shape, structure-function, or spectral constraints. All optional terms are disabled in the maintained presets.

Combined objective

For enabled terms, the implementation forms

\[ \mathcal{L} = w_{base}\mathcal{L}_{base} + g(t)\left( w_{obs}\mathcal{L}_{obs} + w_{inc}\mathcal{L}_{inc} + w_{str}\mathcal{L}_{str} + w_{spec}\mathcal{L}_{spec} \right), \]

where g(t) is the optional auxiliary-only timestep weight. It never rescales the base diffusion term.

Current configured weights are:

Term	Enabled	Weight
Base diffusion/ambient	Yes	1.0
Sparse observation consistency	No	0.25
Sparse profile increments	No	0.1
Structure-function prior	No	0.1
Spectral energy floor	No	0.05
Feature Gram prior	No, unimplemented	0.01 reserved

Base supervision

Standard dense training compares the configured diffusion target with paired GLORYS or the deterministic synthetic target over valid target/ocean support. Ambient training instead uses the original sparse observation support described in Ambient occlusion.

The optional coastal weighting multiplies valid ocean loss near land according to its radius, maximum weight, and ramp. It is disabled in all current pixel presets.

Auxiliary timestep weighting

The local preset enables SNR weighting with minimum 0.1, maximum 1.0, and snr_gamma: 5.0. Since no auxiliary term is enabled, this currently has no numerical effect. It becomes active only when an auxiliary loss is opted in.

The supported modes are:

• snr: derives a normalized, clamped weight from diffusion SNR.
• linear: interpolates between configured noisy- and clean-timestep weights.

Sparse observation consistency

This term applies a Charbonnier penalty between the predicted clean field and observed EN4/ARGO values on valid sparse support:

\[ \rho(r)=\sqrt{r^2+\epsilon^2}. \]

It is an optional extra anchor; ambient base loss already uses sparse observed support in the maintained local objective.

Sparse profile increments

The increment term compares differences between observed pairs rather than absolute values. Vertical adjacent-depth pairs are enabled in its configuration; horizontal pairs are optional. Pair sampling is capped per sample to bound cost.

Structure-function prior

For sampled same-depth pixel pairs separated into distance bins, the second-order structure statistic is based on

\[ S_2(r)=\mathbb{E}[(x(p+r)-x(p))^2]. \]

The loss compares log statistics against either a precomputed reference .pt file (target: reference) or the paired GLORYS target (target: paired_glorys). Reference mode requires reference_path.

Spectral energy floor

This term computes radial spatial-frequency energy and penalizes predicted bands that fall below a configured reference or paired-GLORYS energy floor. It skips the DC band by default and uses a hinge in log-energy space. It is distinct from the post-inference validation exporter in Spectral validation.

Unsupported feature prior

feature_gram_prior reserves configuration for a frozen encoder and reference feature statistics, but the loss is not implemented. Enabling it raises NotImplementedError; documentation and configs must not present it as usable.

Scenario limits

The optional auxiliary implementations operate on scalar temperature or salinity fields. Keep them disabled for --scenario joint unless the implementation and tests are extended to define joint-field semantics.