Conditional Forecasting: Concepts & Methods

• Conditional Forecasting is a framework that defines prediction targets relative to historical data and known future signals, enabling forecasts of means, quantiles, full densities, or counterfactual outcomes.
• It leverages diverse methodologies such as autoregressive models, diffusion-based generation, normalizing flows, and regression-based techniques to capture conditional dependencies in time series.
• Applications span economics, environmental science, and causal analysis, with performance measured by metrics like CRPS, MSE, and quantile losses despite computational and methodological challenges.

Conditional Forecasting (CF) denotes a family of forecasting formulations in which the predictive target is defined relative to explicit conditioning information rather than as an unconditional extrapolation. Across recent work, the condition may be a history window and optional future covariates, a treatment regime in panel causal inference, a query set of future times and channels, a binary mask separating observed and unobserved regions, an auxiliary model output, or a prescribed future scenario. The forecast itself may be a conditional mean, a conditional quantile, a full conditional density, a joint trajectory distribution, or a counterfactual potential outcome. This breadth is visible in formulations such as $p(\mathbf{Y}_f \mid \mathbf{Y}_l, \mathbf{C})$ for multivariate probabilistic forecasting, $\hat p(y \mid x^{\text{obs}}, x^{\text{qu}})$ for irregular query-based prediction, and $\theta_{i,T+h}(w)=E[Y_{i,T+h}(w)\mid \mathcal F_T]$ for counterfactual panel forecasting (El-Gazzar et al., 13 Mar 2025, Yalavarthi et al., 2024, Deb et al., 9 Nov 2025).

1. Conceptual scope and formal definitions

The most common modern use of CF treats forecasting as conditional generative modeling. In this view, a model learns a predictive law over future trajectories given observed history and, when available, exogenous or known future information. FlowTime expresses this directly as

$p(\mathbf{Y}_f \mid \mathbf{Y}_l, \mathbf{C}),$

with $\mathbf{Y}_l$ the past window, $\mathbf{Y}_f$ the forecast horizon, and $\mathbf{C}$ optional covariates (El-Gazzar et al., 13 Mar 2025). CCDM uses essentially the same semantics for multivariate probabilistic forecasting, learning $p_\theta(\mathbf y_0 \mid \mathbf x)$ where $\mathbf x$ is observed history and $\mathbf y_0$ is the future horizon (2410.02168). ProFITi extends the same idea to irregular multivariate time series by conditioning jointly on past observation triples and future queries, targeting the full joint density over the queried future values rather than independent marginals (Yalavarthi et al., 2024).

A second usage emphasizes conditional distributional objects other than the full trajectory law. In realized-volatility forecasting, conditional forecasting is formulated through conditional quantiles: $\hat p(y \mid x^{\text{obs}}, x^{\text{qu}})$0 so that predictors can affect quiet, median, and stressed regimes differently (Bonaccolto et al., 2014). In short-term environmental forecasting, the target is the entire conditional density $\hat p(y \mid x^{\text{obs}}, x^{\text{qu}})$1, modeled via a transformed smooth latent function and a logistic normalization, again making the forecast explicitly conditional on covariates (Huberman et al., 2020). In portfolio risk forecasting, the objects are conditional VaR and ES, with the dependence structure among returns entering through a DCC parameterization (Storti et al., 2022).

A third usage is causal and counterfactual. In FOCUS, CF means forecasting a unit’s future potential outcome under a fixed treatment state given information observed up to time $\hat p(y \mid x^{\text{obs}}, x^{\text{qu}})$2, even though the opposite treatment state is unobserved and induces missingness in the panel. The target is

$\hat p(y \mid x^{\text{obs}}, x^{\text{qu}})$3

and the problem becomes matrix completion with temporal forecasting under a latent factor model (Deb et al., 9 Nov 2025).

Formulation	Conditional object	Representative paper
$\hat p(y \mid x^{\text{obs}}, x^{\text{qu}})$4	Future trajectory distribution	FlowTime (El-Gazzar et al., 13 Mar 2025)
$\hat p(y \mid x^{\text{obs}}, x^{\text{qu}})$5	Conditional quantile function	Realized range quantiles (Bonaccolto et al., 2014)
$\hat p(y \mid x^{\text{obs}}, x^{\text{qu}})$6	Joint future density over queried values	ProFITi (Yalavarthi et al., 2024)
$\hat p(y \mid x^{\text{obs}}, x^{\text{qu}})$7	Counterfactual conditional mean	FOCUS (Deb et al., 9 Nov 2025)

This suggests that CF is not a single algorithmic paradigm but an umbrella for forecasting tasks in which the future object is indexed by explicit side information, constraints, or regimes.

2. Conditioning variables and forecast targets

The conditioning signal varies sharply across domains. In multivariate sequence forecasting, the standard inputs are past observations and known covariates. FlowTime predicts each future $\hat p(y \mid x^{\text{obs}}, x^{\text{qu}})$8 from the last $\hat p(y \mid x^{\text{obs}}, x^{\text{qu}})$9 observations $\theta_{i,T+h}(w)=E[Y_{i,T+h}(w)\mid \mathcal F_T]$0 and corresponding covariates $\theta_{i,T+h}(w)=E[Y_{i,T+h}(w)\mid \mathcal F_T]$1 under an autoregressive factorization of the predictive law (El-Gazzar et al., 13 Mar 2025). Conditional WaveNet defines conditioning causally as forecasting one series using its own past and the past of one or more related series, with separate dilated convolutions applied to the target and each conditioning series (Borovykh et al., 2017). EMFusion similarly conditions future EMF trajectories on a historical window and calendar-based context variables such as Italy_WorkingDay, Italy_WorkingHour, and Italy_Season, injecting them through cross-attention in the denoiser (Yan et al., 17 Dec 2025).

In several formulations, the condition includes future information that is assumed known because it is exogenous or scenario-defined. Temporal financial-network forecasting with DGNN conditions $\theta_{i,T+h}(w)=E[Y_{i,T+h}(w)\mid \mathcal F_T]$2-step-ahead margin forecasts on a pre-specified future stress-test trajectory for the overnight reference rate, so the forecast is made relative to both past contracts and a future rate path (Citterio et al., 2024). In cortical thickness forecasting with SBDM, the condition includes the baseline cortical thickness map, elapsed time to follow-up, and tabular covariates $\theta_{i,T+h}(w)=E[Y_{i,T+h}(w)\mid \mathcal F_T]$3, where age, sex, baseline diagnosis, and follow-up diagnosis jointly specify the predictive context (Stoyanov et al., 10 Sep 2025).

Other papers broaden the conditioning notion further. ProFITi conditions not only on observed history but also on a future query set $\theta_{i,T+h}(w)=E[Y_{i,T+h}(w)\mid \mathcal F_T]$4 of requested channels and times, thereby making the forecast object itself query-dependent (Yalavarthi et al., 2024). CGFM conditions on historical data $\theta_{i,T+h}(w)=E[Y_{i,T+h}(w)\mid \mathcal F_T]$5 and on the output $\theta_{i,T+h}(w)=E[Y_{i,T+h}(w)\mid \mathcal F_T]$6 of an auxiliary forecasting model, using the auxiliary prediction as the source distribution for a corrective flow (Xu et al., 9 Jul 2025). In masked diffusion and inpainting-style models, the condition is the observed region of a structured input. The solar forecasting framework based on conditional DDPM keeps historical rows fixed and treats future rows as the target region to be reconstructed, so the forecast is generated under a mask-defined context rather than a conventional encoder-decoder split (Kiani et al., 27 May 2026).

Counterfactual and missing-data settings add yet another layer. FOCUS conditions simultaneously on observed pre-$\theta_{i,T+h}(w)=E[Y_{i,T+h}(w)\mid \mathcal F_T]$7 panel information and on the treatment/missingness pattern induced by observing only one potential outcome per unit-time pair (Deb et al., 9 Nov 2025). The wind-power FCS framework conditions on the observed part $\theta_{i,T+h}(w)=E[Y_{i,T+h}(w)\mid \mathcal F_T]$8 of a joint feature-target vector and integrates over the missing part, so forecasting is performed by conditional imputation from an inferred joint distribution rather than by conditioning on a fully observed design matrix (Wen et al., 2022).

3. Major methodological families

One prominent CF family is autoregressive probabilistic forecasting. FlowTime factorizes the future predictive law as

$\theta_{i,T+h}(w)=E[Y_{i,T+h}(w)\mid \mathcal F_T]$9

models each factor with a shared conditional flow, and samples autoregressively by solving an ODE from Gaussian base noise at each step (El-Gazzar et al., 13 Mar 2025). This combines classical sequential conditioning with conditional flow matching. A related but non-flow example appears in conditional WaveNet, where causal dilated convolutions provide a large receptive field while conditioning series are handled by parallel convolutions and learned skip connections (Borovykh et al., 2017).

A second family is diffusion- or flow-based conditional generation. CCDM uses a conditional DDPM reverse process $p(\mathbf{Y}_f \mid \mathbf{Y}_l, \mathbf{C}),$0 with a channel-aware denoiser and a denoising-based temporal contrastive objective that explicitly targets predictive mutual information $p(\mathbf{Y}_f \mid \mathbf{Y}_l, \mathbf{C}),$1 (2410.02168). EMFusion also uses conditional DDPM, but augments a residual U-Net with cross-attention and an imputation-based sampling strategy so that forecasting is treated as structural inpainting under irregular measurements (Yan et al., 17 Dec 2025). FlowCast replaces diffusion with Conditional Flow Matching in latent space, learning a vector field that transports Gaussian latent noise to future radar-latent trajectories conditioned on past radar observations (Ribeiro et al., 12 Nov 2025). T-CFM does the same for trajectory forecasting, learning a solver time-varying vector field $p(\mathbf{Y}_f \mid \mathbf{Y}_l, \mathbf{C}),$2 and sampling by integrating the learned ODE rather than running a long denoising chain (Ye et al., 2024).

A third family comprises conditional normalizing-flow approaches. ProFITi models the joint future density over irregularly queried values using a conditional normalizing flow with invertible triangular attention, an invertible elementwise linear layer, and the Shiesh activation, while enforcing permutation invariance over query order (Yalavarthi et al., 2024). CANF takes a different route: it first fits a normalizing flow to the full joint sequence $p(\mathbf{Y}_f \mid \mathbf{Y}_l, \mathbf{C}),$3, then approximates the learned distribution with a Gaussian mixture model so that the desired conditional multi-step distribution $p(\mathbf{Y}_f \mid \mathbf{Y}_l, \mathbf{C}),$4 can be computed analytically (Jamgochian et al., 2022).

A fourth family is semi-parametric and regression-based. Conditional quantile forecasting for realized range volatility estimates quantile-specific coefficients $p(\mathbf{Y}_f \mid \mathbf{Y}_l, \mathbf{C}),$5 by minimizing the Koenker–Bassett asymmetric absolute loss, allowing predictors such as lagged volatility, $p(\mathbf{Y}_f \mid \mathbf{Y}_l, \mathbf{C}),$6, $p(\mathbf{Y}_f \mid \mathbf{Y}_l, \mathbf{C}),$7, and jumps to have heterogeneous effects across quantile levels (Bonaccolto et al., 2014). Semi-DCC estimates conditional portfolio VaR and ES using a two-step procedure based on a strictly consistent joint VaR-ES loss while embedding dependence through dynamic conditional correlations (Storti et al., 2022). The nonparametric conditional density framework for short-term forecasting instead parameterizes a smooth latent score $p(\mathbf{Y}_f \mid \mathbf{Y}_l, \mathbf{C}),$8 and transforms it into a conditional density via

$p(\mathbf{Y}_f \mid \mathbf{Y}_l, \mathbf{C}),$9

with polynomial or deep-learning realizations and a case-control approximation to the normalization integral (Huberman et al., 2020).

4. Counterfactual, missing-data, and irregular-observation formulations

Counterfactual panel forecasting makes the conditional structure inseparable from missingness. FOCUS assumes a low-rank factor model

$\mathbf{Y}_l$0

and a stable VAR(1) law for the latent factors,

$\mathbf{Y}_l$1

The procedure first estimates factors and loadings from the partially observed panel through a PCA-type matrix-completion estimator and then estimates $\mathbf{Y}_l$2 by OLS to produce the $\mathbf{Y}_l$3-step forecast $\mathbf{Y}_l$4 (Deb et al., 9 Nov 2025). The paper derives a high-probability forecast error bound and asymptotic normality under stationary stochastic dynamics, with the asymptotic variance decomposing into factor/loading estimation error and VAR-forecasting error.

Missing features can also be treated as part of the forecasting problem itself. In the wind-power FCS framework, a full observation is $\mathbf{Y}_l$5, missingness is encoded by $\mathbf{Y}_l$6, and forecasting is performed by iteratively sampling from conditional models $\mathbf{Y}_l$7 in a fully conditional specification loop. Under MAR, the method aims to infer the joint distribution $\mathbf{Y}_l$8 from incomplete data and then obtain the predictive density by marginalization over missing covariates (Wen et al., 2022). Operationally, repeated imputations of all missing entries, including the target, produce an empirical predictive distribution.

Irregularly sampled multivariate time series require a different notion of conditionality. ProFITi represents observations as sparse triples $\mathbf{Y}_l$9 and future requests as query pairs $\mathbf{Y}_f$0, then learns the joint density of the corresponding answers $\mathbf{Y}_f$1 (Yalavarthi et al., 2024). Because the model forecasts arbitrary query sets rather than a fixed contiguous horizon, the conditional forecast is defined relative to a variable-size request specification.

Masked generative models move in a similar direction by converting forecasting into inpainting. The multivariable solar forecasting framework reformulates future time steps as missing rows within a 2D patch representation and applies a conditional DDPM with mask

$\mathbf{Y}_f$2

so that the observed historical region remains clean while only the future region is corrupted and reconstructed (Kiani et al., 27 May 2026). EMFusion applies a closely related inpainting logic during reverse diffusion by clamping observed EMF values back into the sample at each denoising step (Yan et al., 17 Dec 2025). This suggests a convergence between missing-data modeling and conditional forecasting in high-dimensional sequence generation.

5. Guidance, scenarios, and counterfactual control

Several recent CF models are explicitly designed to forecast under guidance from external mechanisms or hypothetical regimes. CGFM starts from an auxiliary forecast $\mathbf{Y}_f$3 rather than pure noise and learns a conditional flow from the auxiliary prediction distribution to the true future distribution. Its conditional path

$\mathbf{Y}_f$4

can use CondOT, Poly-$\mathbf{Y}_f$5, LinearVP, or Cosine schedules, and the paper reports that $\mathbf{Y}_f$6-prediction works best empirically for forecasting (Xu et al., 9 Jul 2025). The central claim is not merely that the future depends on history, but that the residual structure of a prior forecaster can itself be exploited as conditioning information.

Stress-testing applications make the scenario variable fully explicit. The DGNN framework for margin forecasting conditions on a future interest-rate path generated from a CIR process, while the network topology of IRS/OIS contracts evolves with the same reference rate. The target is the node-level net variation margin over horizons up to $\mathbf{Y}_f$7, and the paper emphasizes that conditioning on the future rate path is essential; without it, the model tends toward predicting near-zero expected variation margins (Citterio et al., 2024). This is a strict scenario-conditioned use of CF.

Counterfactual generation can also invert the forecasting relation. ForecastCF begins from a fixed trained forecaster $\mathbf{Y}_f$8 and searches for a modified input series $\mathbf{Y}_f$9 such that the output forecast lies inside user-specified lower and upper bounds $\mathbf{C}$0. The optimization acts on the input series, with a validity mask focusing gradients only on horizon steps whose predictions violate the desired range (Wang et al., 2023). The paper describes this as counterfactual generation for time series forecasting; a plausible implication is that it operationalizes CF as an inverse design problem rather than a direct predictive one.

In biomedical forecasting, SBDM uses a bidirectional conditional Brownian bridge diffusion process to generate individualized cortical-thickness trajectories from a baseline cortical map and tabular conditions, and further demonstrates factual and counterfactual trajectories by altering follow-up diagnosis labels (Stoyanov et al., 10 Sep 2025). The baseline map is embedded into the bridge itself rather than supplied merely as side information. This makes the conditioning variable partly geometric and partly clinical.

The hybrid PV framework uses the term CF in a narrower operational sense. There, CF denotes the cloud-event forecasting module that conditions short-horizon PV predictions on normalized historical irradiance from a detector network of neighboring sites selected by scenario-based correlation analysis. The detector network is intended to capture leading cloud events that reach the target site later, and a third TCN then reconciles this conditional forecast with a physics-based trend forecaster (Li et al., 2021).

6. Evaluation criteria, empirical regularities, and limitations

Because CF spans conditional means, densities, trajectories, and counterfactuals, its evaluation criteria are correspondingly heterogeneous. Probabilistic sequence models are commonly evaluated with CRPS, NRMSE, MSE, MAE, or njNLL. FlowTime reports improvements in NRMSE on all five dynamical systems for both prediction and extrapolation, and usually improves CRPS as well (El-Gazzar et al., 13 Mar 2025). ProFITi uses normalized joint negative log-likelihood to assess whether the full joint future density is captured rather than only marginal forecasts (Yalavarthi et al., 2024). EMFusion reports CRPS, PICP, NRMSE, ND, RMSE, MAPE, and Energy Score for frequency-selective EMF forecasting (Yan et al., 17 Dec 2025).

Empirical studies repeatedly associate better CF performance with architectures that preserve the structure of the conditioning information. FOCUS outperforms mSSA and SyNBEATS when latent factors are autoregressive, and its HeartSteps application shows that exploiting latent temporal dependence helps forecast counterfactual responses in longitudinal interventions (Deb et al., 9 Nov 2025). FlowCast reports that CFM with 10 steps is more accurate and more efficient than DDIM with 10, 50, or 100 steps on the same architecture, with lower CRPS and higher CSI/HSS on SEVIR (Ribeiro et al., 12 Nov 2025). EMFusion with working-hour conditioning outperforms the best baseline by 23.85% in CRPS and 13.93% in NRMSE, while also reducing prediction CRPS error by 22.47% (Yan et al., 17 Dec 2025). SBDM achieves the lowest vertex-wise MAE on both ADNI and OASIS among the compared cortical-thickness forecasters (Stoyanov et al., 10 Sep 2025).

In financial and risk-oriented CF, evaluation remains explicitly conditional on the forecast object. Realized-range quantile forecasting is assessed with the Berkowitz test, the Amisano–Giacomini weighted log-score comparison, and Diebold–Mariano quantile-loss comparisons, reflecting the fact that the output is a conditional density or quantile family rather than a point forecast (Bonaccolto et al., 2014). Semi-DCC uses quantile loss, AL and FZ0 joint losses, Model Confidence Set analysis, and VaR/ES backtests such as UC, CC, DQ, VQR, and ESR variants (Storti et al., 2022).

The literature also states several recurring limitations. Diffusion-based CF can be computationally heavy because iterative denoising requires many function evaluations; FlowCast is motivated directly by that bottleneck in time-critical nowcasting (Ribeiro et al., 12 Nov 2025). FCS-based forecasting depends on the MAR assumption for missingness (Wen et al., 2022). Counterfactual bridge models such as SBDM require a baseline scan and cannot directly validate hypothetical counterfactual trajectories (Stoyanov et al., 10 Sep 2025). The solar inpainting framework reports strongest performance for short-term horizons and smooth degradation as the target region grows (Kiani et al., 27 May 2026). Conditional WaveNet notes that gains from conditioning shrink when inter-series dependencies weaken (Borovykh et al., 2017). These constraints indicate that, although CF is broadly applicable, the value of conditioning depends materially on whether the supplied context carries predictive structure, whether that structure is represented faithfully by the model class, and whether the computational budget permits conditioning to be exploited at inference time.