🤖 machine learning

SPLICE: Latent Diffusion over JEPA Embeddings for Conformal Time-Series Inpainting

SPLICE is a modular framework that combines latent diffusion over JEPA embeddings with Adaptive Conformal Inference to achieve state-of-the-art time-series imputation accuracy and distribution-free, finite-sample reliability guarantees for critical power system applications.

Original authors: Arnaud Zinflou

Published 2026-05-04

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Arnaud Zinflou

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to listen to a favorite song, but a chunk of the recording is missing. Maybe the tape got chewed up, or the Wi-Fi cut out for a few days. You need to fill in that missing part so the song plays smoothly, but you also need to know: How sure are we that what we filled in is actually what was there?

This paper introduces SPLICE, a new tool designed to fix missing chunks of electricity data (like a song's missing notes) while also giving a "confidence score" for the fix. Here is how it works, broken down into simple parts:

1. The Problem: The "Static" in the Data

Power grids need to know exactly how much electricity is being used every hour to keep the lights on. But sometimes, sensors break, cables get cut, or computers crash, leaving huge gaps in the data (sometimes missing for 91 days straight!).

Old methods tried to fill these gaps by just drawing a smooth line between the "before" and "after" points. It's like guessing the missing lyrics of a song by just humming the tune between the known words. It looks okay, but it misses the complex rhythm and details needed to run a power grid safely.

Newer AI methods can guess the missing details better, but they are like a confident artist who guesses the lyrics perfectly but refuses to admit, "I might be wrong." In a power grid, being wrong without knowing it can be dangerous.

2. The Solution: SPLICE (The "Dreaming" Architect)

The authors built a system called SPLICE that acts like a highly trained architect who doesn't just guess; they "imagine" what the missing building should look like based on the surrounding neighborhood.

Here is the step-by-step process:

Step 1: The Translator (JEPA Encoder)
Imagine the electricity data is a complex language. The first part of SPLICE is a translator that takes a whole day of electricity usage and compresses it into a tiny, 64-number "summary note." It learns the vibe of the day (is it a hot summer Tuesday? a quiet winter weekend?) without getting bogged down in every single detail. This is based on a concept called JEPA (Joint Embedding Predictive Architecture), which is like teaching a computer to understand the "story" of the data rather than just memorizing the numbers.
Step 2: The Bridge Builder (Conditional Latent Bridge)
Once the system has the "summary notes" for the days before and after the gap, it needs to build a bridge across the missing days.
- The Deterministic Bridge: This is the "safe" guess. It builds the most likely path across the gap, like drawing the straightest line between two points.
- The Creative Bridge (Flow Matching): This is the "dreaming" part. Instead of just drawing one line, it generates many possible paths the electricity usage could have taken. It's like imagining ten different versions of the missing song lyrics. The paper found a new, faster way to do this (called Flow Matching) that is 5 to 10 times quicker than older methods but just as accurate.
Step 3: The Translator Back (Decoder)
The system takes those "summary notes" and the "bridge" it built and translates them back into real, hourly electricity numbers. Crucially, it looks at the weather and calendar (is it raining? is it a holiday?) to make sure the guess makes sense for that specific time.

3. The Safety Net: ACI (The "Confidence Band")

This is the most important innovation. Even the best guess can be wrong.

Old Way: The system would give you a single number and say, "This is the missing data."
SPLICE's Way: It wraps the answer in a safety band. It says, "We think the missing data is here, but we are 95% sure it's somewhere inside this wide band."

The system uses a technique called Adaptive Conformal Inference (ACI). Think of this as a self-correcting thermostat.

If the system starts guessing too narrowly and missing the real data, the ACI automatically widens the safety band.
If it's being too cautious and the band is huge, it tightens it up.
It does this in real-time, learning from its mistakes as it goes, ensuring that over the long run, the real data falls inside the band 93–95% of the time.

4. The Results: Better Guesses, Faster, and Safer

The authors tested this on 13 different electricity datasets (from homes, factories, and cities).

Accuracy: SPLICE made the most accurate guesses of missing data compared to five other top methods. It won on 9 out of 12 datasets.
Speed: By using the new "Flow Matching" method, it filled in 91 days of missing data in just a few milliseconds, which is 5 to 10 times faster than the previous best methods.
Reliability: It fixed the "under-coverage" problem. Older methods often claimed to be 95% confident but were actually only right 86% of the time. SPLICE corrected this, hitting the 93–95% target consistently.

5. The "One-Size-Fits-All" Trick

Finally, the paper showed that the "Translator" (the part that understands the data) could be trained on nine different cities and then used on four new cities it had never seen before. It worked almost as well as if it had been trained specifically on those new cities. This means the system is flexible and can be deployed quickly without needing to retrain everything from scratch.

In summary: SPLICE is a smart, fast, and honest tool. It doesn't just fill in the blanks of missing electricity data; it imagines the most likely scenarios, does it incredibly fast, and puts a safety net around its answers so engineers know exactly how much they can trust the result.

1. Problem Statement

The paper addresses the critical challenge of long-horizon time-series imputation in power systems, specifically for reconstructing missing electricity load data due to sensor failures or communication outages.

The Gap: Existing deep generative models (e.g., diffusion models, VAEs) achieve high reconstruction accuracy but lack finite-sample reliability guarantees. In safety-critical infrastructure like power grids, point estimates without uncertainty quantification are insufficient for dispatch and planning.
The Challenge: Traditional interpolation fails to capture fine-grained temporal structures, while standard conformal prediction methods often fail under non-stationary distribution shifts (e.g., seasonal changes, weather regime shifts) because they assume data exchangeability.
Goal: Develop a framework that provides high-fidelity reconstruction of missing data (up to 91 days) while offering distribution-free, adaptive prediction intervals with rigorous coverage guarantees.

2. Methodology: The SPLICE Framework

SPLICE (Self-supervised Predictive Latent Inpainting with Conformal Envelopes) is a modular, four-stage pipeline:

A. JEPA Encoder (Representation Learning)

Architecture: Uses a Joint Embedding Predictive Architecture (JEPA) to map daily multivariate segments (load, weather, calendar) into a compact 64-dimensional latent space.
Mechanism: A masked Transformer predicts the latent embedding of masked days based on observed context.
Training Objective: Combines cosine prediction loss with VICReg-style regularization (variance and covariance constraints) to prevent embedding collapse and ensure information spreading.
Advantage: Unlike VAEs, JEPA learns a structured latent space that preserves temporal dynamics without the "blurring" effect of reconstruction losses, making it ideal for long-horizon generation.

B. Conditional Latent Bridge (Trajectory Generation)

Function: Generates candidate trajectories for the missing gap within the JEPA latent space.
Modes: Supports four stochasticity levels:
1. Deterministic: Direct prediction (lowest MSE).
2. Noise-perturbed: Adds Gaussian noise to the deterministic output to create an ensemble for uncertainty quantification.
3. Generative (DDIM): Standard diffusion sampling.
4. Generative (Flow Matching): The preferred backend. It learns a velocity field to transport samples along straight ODE paths.
Efficiency: The Flow Matching variant achieves quality comparable to DDIM in 5–10 Euler steps, offering a 5–10× speedup over the 50-step DDIM sampler.

C. Hourly-Conditioned Decoder

Function: Maps the generated latent trajectories back to the signal space (hourly load).
Innovation: Unlike standard decoders, it is conditioned on hourly covariates (weather, calendar) during the gap. This allows the model to "know" the external factors (e.g., temperature) for the missing days, closing the information gap between latent and observation spaces.
Training: Uses a Load-weighted MSE loss (5× weight on load) and noise augmentation to improve robustness.

D. Adaptive Conformal Inference (ACI)

Problem: Standard Conformal Prediction (CQR) assumes exchangeability, which is violated in time series.
Solution: SPLICE wraps the generative output with Adaptive Conformal Inference (ACI).
Mechanism: ACI maintains a running miscoverage level ( $\alpha_t$ ) that updates online based on observed errors:
$\alpha_{t+1} = \alpha_t + \gamma(\alpha - \text{err}_t)$
Guarantee: This ensures long-run coverage (e.g., 95%) even under distribution shifts, self-correcting without manual recalibration.

3. Key Contributions

Modular Latent Pipeline: A novel architecture coupling JEPA representation learning with a conditional latent bridge and an hourly-conditioned decoder.
Flow Matching Efficiency: Demonstrates that Flow Matching in JEPA latent space provides a 5–10× inference speedup over DDIM with comparable or better quality.
Distribution-Free Uncertainty: First work to wrap a deep generative imputation pipeline with ACI, correcting under-coverage failures of up to 7.5 percentage points in non-stationary environments.
Transfer Learning: Shows that a single pooled JEPA encoder trained on nine diverse domains can transfer to four unseen domains with minimal fine-tuning (only the bridge and decoder), matching or exceeding per-dataset oracles.

4. Experimental Results

Evaluated on 13 datasets (9 proprietary utility feeds, 3 UCI Electricity, 1 ETTh1) with 91-day gaps:

Accuracy:
- Achieved the lowest mean Load-only MSE (0.056), outperforming strong baselines like SAITS (0.064), BRITS (0.068), and CSDI (0.252).
- Won 9/12 non-degenerate datasets against external baselines.
- Flow Matching reduced MSE by 8.7% compared to DDIM while using 10× fewer steps.
Uncertainty Calibration:
- ACI achieved 93–95% empirical coverage across all datasets, successfully fixing under-coverage in volatile datasets (e.g., RIInd1014 improved from 86% to 93.5%).
- CRPS (Continuous Ranked Probability Score): The noise-perturbed ensemble achieved the best CRPS (0.161), an 18.3% improvement over the strongest deterministic baseline (SAITS).
Transferability:
- A pooled encoder fine-tuned only on the bridge/decoder matched or exceeded per-dataset oracles on 3 out of 4 held-out domains.
Ablation Studies:
- JEPA embeddings reduced MSE by 53.2% compared to JEPA-only and 25.1% compared to a legacy VAE+Bridge baseline.
- The enhanced decoder (Load-weighted loss + noise augmentation) contributed an additional 9.3% MSE reduction.

5. Significance and Impact

Grid Reliability: Provides power grid operators with not just imputed values, but statistically guaranteed confidence intervals, crucial for preventing under-provisioning or missed demand response events.
Scalability & Efficiency: The Flow Matching backend makes long-horizon imputation computationally feasible for real-time or near-real-time applications.
Generalization: The pooled encoder approach suggests a path toward universal time-series foundation models, reducing the cost of training new models for every new sensor or region.
Methodological Advance: Successfully bridges the gap between generative modeling (for high-fidelity reconstruction) and conformal prediction (for rigorous uncertainty), addressing a major limitation in current AI-driven infrastructure management.

In conclusion, SPLICE represents a significant step forward in time-series imputation by combining the representational power of JEPA, the efficiency of Flow Matching, and the statistical rigor of Adaptive Conformal Inference to solve a critical problem in energy systems.