High-quality time series (TS) data is essential for reliable analytics, forecasting, and knowledge-driven systems. In operational settings, however, TS are frequently degraded by missing values arising from sensor faults, intermittent connectivity, maintenance activities, and extended partial-blackout events. Whilst recent difusionbased models have improved imputation accuracy, they remain largely signal-centric, make limited use of semantic and operational metadata, and provide little support for data quality considerations.
Imagine a city relying on a network of trafic sensors to manage congestion in real time. When multiple sensors fail due to maintenance or network disruptions, the system must reconstruct missing measurements to make safe and eficient decisions. Similarly, satellite time series TS used for vegetation monitoring or climate analysis are frequently incomplete due to cloud cover, sensor outages, or acquisition constraints. In both cases, missing time series values threaten operational reliability, safety, and trust in downstream analytics and decision-making pipelines.
Classical imputation methods use interpolation and state-space models [
CEUR Workshop
ISSN1613-0073 ifxed topologies derived from distance metrics or learned correlations. Neither can systematically access operational constraints that determine which conditioning sources are semantically valid.
Moreover, they operate on raw signal values and remain signal-centric. Relevant dependencies are either assumed observable in the data or implicitly learnable from correlations. In practice, many critical relationships are implicit and external to the signal [13, 12]. For instance, sensor networks contain structured metadata that is not present in raw measurements, including device specifications, operational logs, and quality assessments. This metadata determines which sensors provide valid conditioning context. Optical and radar satellites measure diferent physical properties. Using radar to impute optical observations may produce smooth interpolations that violate spectral consistency. A recently recalibrated sensor may have shifted its measurement baseline. Conditioning on its historical values introduces bias. As such, when context is absent or implicit, imputation models may produce statistically plausible but operationally invalid reconstructions. Specifically, difusion models may condition on unreliable or invalid sources.
These failures may well occur in reality. In trafic management, imputing flow measurements from a highway sensor using an unrelated arterial sensor can overestimate throughput capacity, triggering unsafe signal timing decisions. In satellite-based crop monitoring, conditioning optical vegetation indices on radar input produces incoherent values that misclassify crop health, propagating errors into yield forecasts. When such imputed values are ingested into knowledge graphs for downstream reasoning, the damage compounds. Invalid upstream reconstructions become trusted facts in the graph, silently degrading every query and inference built on them. These failure modes cannot be resolved by improving model capacity alone. They require access to external metadata to determine which sources are semantically valid for conditioning.
To address this gap, we envision a metadata- and governance-aware framework for TS imputation. The system combines a metadata knowledge graph (KG), subgraph-conditioned difusion, and large language model (LLM)-based orchestration. This vision directly addresses key challenges in hybrid KG–LLM ecosystems by improving the fidelity of data streams feeding KGs, reducing downstream reasoning errors caused by poor upstream data quality, and supporting human-in-the-loop governance [10].
Our central hypothesis is that externalising implicit relationships in a KG and conditioning difusion
models on quality-filtered subgraphs improves imputation under structured missingness, heterogeneous
sensors, and evolving operational conditions. Learning-based models capture temporal and
crossvariable patterns from observed data. They cannot infer operational semantics, provenance, or quality
constraints that are not present in raw signals [
TS imputation has been widely studied. Classical imputation methods include interpolation, Kalman
filtering, and state-space models [
Graph-based methods propagate information across correlated sensors using GNNs, hypergraphs, or
attention mechanisms [
A parallel line of work uses knowledge graphs to encode structured metadata, provenance, and relational constraints [14, 15]. Recent research explores LLMs as orchestrators for KG workflows, including construction from unstructured text, subgraph selection, and explanation generation [17, 18]. Prior work focuses on KG construction, completion, retrieval-augmented generation, and post-hoc reasoning, with few approaches guiding TS imputation or producing auditable quality narratives.
Existing methods address generative modelling, relational reasoning, or workflow orchestration independently. The proposed paradigm combines difusion-based imputation, metadata-driven KG, and LLM orchestration in a single framework for governed TS reconstruction.
The framework comprises three-layer hybrid system operating on diferent data representations. The metadata knowledge graph maintains sensor specifications, quality indicators, and relationships. Difusion models generate imputations conditioned on observed measurements and graph-derived context. LLM agents query the graph, configure imputation parameters, and produce audit trails. Figure 1 shows the data flow. When imputation is requested for sensor at time , the system would extract a quality-filtered subgraph sub containing candidate conditioning sensors. A graph neural network computes embeddings injected into the difusion model’s denoising process. Generated samples are validated against metadata graph constraints. An LLM agent documents which sensors were retained, and why.
The metadata knowledge graph would store sensor properties, quality indicators, and operational constraints. Raw TS remain in specialised time-series databases. This separation addresses scalability using a graph database (such as Neo4j) that handles thousands of sensor entities and their relationships, whilst numerical storage manages high-frequency measurements. Sensors are represented as nodes with attributes such as measurement type, physical units, operating range, calibration dates, and reliability indicators. Contextual entities capture geographic regions, infrastructure components, and asset hierarchies. Edges encode relationships such as spatial proximity, network topology, functional similarity, and maintenance dependencies, while partitions summarise similar behaviors or dynamics.
From a technical perspective, the KG uses a lightweight property-graph schema rather than a full ontology. Core node types include Sensor, MeasurementType, Location, Asset, and QualityEvent.
Sensor nodes store attributes such as modality, physical units, operating range, calibration date, and reliability indicators. Edges encode MEASURES, LOCATED_IN, ADJACENT_TO, FUNCTIONALLY_RELATED, and AFFECTED_BY, enabling traversal over specified relationships. Quality constraints are enforced using query-level filtering, allowing the schema to evolve with operational needs.
In doing so, the graph externalises relationships that learning-based models cannot infer from raw signals. A GNN trained on TS may learn that sensors A and B are correlated. It cannot determine whether A measures temperature in Celsius whilst B measures humidity as a percentage, rendering them semantically incompatible for direct conditioning. The graph encodes modality explicitly. Crucially, the system maintains an explicit, queryable, and evolvable representation of metadata without handling highvolume numerical data, enforcing a clean separation between statistical reconstruction and semantic reasoning.
For each imputation task targeting sensor over time window [ 1, 2], we extract a task-specific subgraph sub = ( sub, sub) that defines admissible conditioning context. Candidate neighbors are first identified through graph traversal over spatial, topological, and similarity relations, and then filtered based on quality indicators (e.g., missingness rates, anomaly flags) and semantic compatibility (e.g., sensor modality or measurement units).
This approach replaces heuristic neighbor selection (e.g., -nearest by distance) with metadatagoverned decisions. Each edge in sub has an explicit justification, and operators can inspect, override, or revise these rules through graph queries without retraining the difusion model. Thresholds and traversal depth are configurable at query time, enabling transparent and auditable context selection. Using metadata for subgraph extraction, the framework ensures that conditioning context is semantically and operationally valid. This enables flexibility and explainability in the imputation process.
In standard difusion-based TS imputation, denotes the noisy latent at difusion step and obs the observed measurements. The model learns the reverse process:
( −1 ∣ , obs).
Our framework extends this formulation by conditioning the generation process on the metadata subgraph:
( −1 ∣ , obs, sub).
Embeddings of sub are calculated using a graph neural network that encodes relational structure, quality indicators, and semantic attributes. These embeddings are injected into the difusion model’s denoising network. Implementation options include concatenation with intermediate features, cross-attention mechanisms, or message-passing layers. The choice depends on the specific difusion architecture and computational constraints.
Constraint enforcement combines soft penalties during training with hard clipping at sampling time.
Let ℒdifusion denote the standard difusion objective and ℒconstraint a penalty for violations of sensor-specific bounds [ min, max] encoded in the metadata graph. The resulting training objective is ℒ = ℒdifusion + ℒ constraint.
This design allows the knowledge graph and difusion model to evolve independently. Adding new sensor types requires updating graph schema, not retraining the denoising network. Changing quality thresholds modifies subgraph extraction rules without touching model parameters.
LLMs orchestrate the imputation pipeline through specialised agents that query the knowledge graph and coordinate workflow steps.
The KG-construction agent updates metadata from maintenance logs, calibration records, and operational documentation. It parses unstructured text to extract structured facts and writes them to the graph whilst tracking provenance.
The imputation-planning agent receives imputation requests and queries the graph for candidate conditioning sensors. It adapts subgraph extraction based on missingness patterns and metadata quality.
The quality-assessment agent evaluates generated reconstructions against metadata-derived constraints. It checks whether values fall within valid operating ranges, assesses temporal consistency with adjacent observations, and compares against ground truth when available. Quality metrics are written back to the graph as provenance records.
The explanation agent generates human-readable narratives documenting imputation decisions. For each reconstruction, it describes which sources, constraints, and reliability factors influenced each imputation. Explanations reference only entities and attributes retrieved from the graph to prevent hallucinated claims.
Agent interactions with graph databases use generated Cypher queries. To ground LLM outputs in factual metadata, agents receive graph query results in their prompts and are constrained to reference only retrieved entities. If an agent generates ungrounded claims, the system detects this through entity linking and retries with stricter constraints. Agent interactions follow a retrieve-then-generate pattern. For each task, the relevant agent first issues a structured query to retrieve candidate entities and their attributes from the KG. The query results are then injected into the agent’s prompt as the sole factual context. To prevent hallucination, agent outputs undergo entity-linking verification and every sensor, attribute, or event referenced in the response is checked against the query result set. If ungrounded references are detected, the agent is re-prompted with the specific violation. This retrieve-constrainverify loop applies uniformly across all agents. The orchestration layer provides transparency for human oversight and structured provenance for downstream reasoning. The modular agent design allows individual components to be updated or replaced as LLM capabilities evolve.
Components operate at distinct abstraction levels. The KG provides a task-specific quality-filtered subgraph. A lightweight GNN encodes this subgraph into embeddings representing semantic compatibility, quality indicators, and relational structure. LLM agents orchestrate the workflow and generate explanations grounded in KG facts but do not participate in numerical generation.
Consider a satellite-derived TS for a fixed geographic tile observed across five acquisition times. Four cloud contamination, creating structured corruption as shown in Table 1. sources provide measurements: a primary optical sensor 1, an auxiliary optical sensor 2, a radar sensor , and an adjacent tile observed by 1. At time 3, the measurement from 1 is invalid due to
Let denote the multivariate series over { 1, 2, , } excluding 1( 3). A task-specific metadata subgraph sub is extracted from the knowledge graph in Figure 2 by retaining only semantically compatible and quality-valid sensors. In this example, 2 and constitute admissible conditioning signals, while 1 is excluded due to cloud invalidation and due to modality incompatibility with optical vegetation indices. Conditioning the difusion model on ( obs, sub) yields a posterior distribution over the missing value. The imputed value ̂ KG ( 3) is interpreted as a point summary (e.g., conditional mean, MAP) derived under KG-governed context selection. Raw observations alone do not explain why 1( 3) is missing nor which alternative sources should be trusted. The metadata KG provides essential context: (i) 1( 3) is flagged as invalid due to cloud contamination, (ii) is a radar sensor and therefore not compatible with optical reflectance, and (iii) the adjacent tile exhibits historically strong spatial afinity with the target tile. Figure 2 illustrates how these semantic constraints are encoded and operationalised for context selection. A signal-centric approach would average all available sources, including semantically incompatible ones such as , leading to biased or incoherent estimates. In contrast, the framework excludes invalid sources and conditions only on admissible signals. This estimate respects temporal continuity and is accompanied by explicit, metadata-grounded justification. This example illustrates how metadata knowledge graphs encode provenance, quality, and semantic constraints that are absent from raw observations. For illustration, a simplified weighted combination gives: ̂ KG ( 3) = 0.7 ⋅ 2( 3) + 0.3 ⋅ ( 3) = 0.623.
and obs the set of all observed entries
This framework demonstrates how KGs can govern generative imputation in operational data systems. Three architectural decisions distinguish this approach from signal-only methods. Difusion models receive explicit semantic constraints rather than inferring them from correlations. This is expected to improve robustness when training correlations are absent, misleading, or outdated. The KG externalises what models cannot learn from measurements alone [13].
Statistical reconstruction, semantic validation, and workflow coordination operate independently. New sensors, updated calibration schedules, or revised quality policies modify graph content without retraining difusion models. Human operators inspect and override subgraph extraction rules through graph queries. This modularity supports adaptation in evolving deployments. Additionally, LLM agents document which sensors were included or excluded, which constraints were enforced, and which quality measures determined subgraph membership. Explanations reference graph entities, enabling systems to trace provenance.
The framework addresses a gap in hybrid KG–LLM ecosystems by allowing metadata governance at the imputation stage. This reduces the risk of poor TS fidelity propagating errors into reasoning systems. The design pattern generalises beyond TS. Domains where raw measurements require semantic validation (medical sensors, financial data, environmental monitoring) could apply metadata-conditioned generation. The specific technologies (Neo4j, difusion models, LLM agents) are instantiation choices. The principle is separating what models learn from data, from what systems enforce through metadata.
The proposed approach is designed to minimise training and fine-tuning overhead. Difusion models are trained or reused independently of the knowledge graph and LLM components. The graph neural network operates on compact subgraphs rather than the full metadata graph to lower inference costs. Since metadata evolves more slowly than raw time series, graph embeddings can be cached or incrementally updated. LLMs are only used at inference time without fine tuning. The approach is feasible in environments where retraining large models is costly or impractical. It is most valuable in domains where structured metadata exists alongside time series measurements, sensors are heterogeneous in their characteristics, and governance is required. For homogeneous univariate time series without operational metadata, the metadata layer adds limited value and standard imputation methods could sufice. The framework’s benefit scales with metadata richness. The more operational context is available in the KG, the greater the improvement over traditional approaches. The specific technology choices are instantiation decisions, and the core principle of separating statistical reconstruction from metadata-governed context selection is architecture-agnostic.
This vision paper opens research directions for difusion-based time series imputation by explicitly integrating metadata as conditioning context. Existing difusion models learn temporal dependencies from observed correlations but cannot infer operational semantics, quality constraints, or provenance from raw measurements. We propose externalising this knowledge in queryable graphs and conditioning generation on quality-filtered subgraphs. This reframes imputation as a process constrained by semantic validity and not temporal plausibility alone.
Implementation is underway integrating KGs with difusion-based imputation models. Evaluation will assess whether metadata and KG-conditioned imputation improves robustness on real-world datasets, including both regular and irregular time series. Envisaged baselines include Yun et al. [8] and Difusion-TS [ 16]. Considered metrics for evaluation will include RMSE/MAE, metadata-aware criteria covering constraint violations, structured missingness robustness, and fidelity of LLM-generated explanations.
Notable challenges remain open. Subgraph extraction and graph embedding add computational overhead. This calls for latency analysis for high-frequency streams, and caching/incremental updates need exploration. The framework assumes reasonably accurate metadata, yet operational systems contain outdated calibration records, incorrect specifications, and stale quality indicators. Degradation under these errors remains an open problem. Potential approaches include uncertainty-aware graph queries, metadata validation pipelines, and human-in-the-loop verification for high-stakes imputations. Similarly, explanation agents must avoid hallucinating facts not present in the knowledge graph. Structured generation and constrained decoding may improve reliability, but formal verification that references only retrieved entities is still unsolved.
Existing imputation benchmarks measure reconstruction error on held-out test data, but do not assess semantic validity, explainability quality, or governance efectiveness. Evaluation frameworks capturing these dimensions are needed.
Additionally, sensor networks lack common vocabularies for quality indicators, calibration procedures, and operational constraints. Domain-specific ontologies exist, but integrating heterogeneous deployments requires schema alignment and entity resolution. KG construction from unstructured logs remains a challenging extraction problem.
These challenges define a research agenda for trustworthy imputation in operational settings. Translating this vision into production systems requires addressing computational eficiency, metadata quality assurance, and evaluation protocols that measure semantic validity and auditability beyond reconstruction error.
This work was supported by the Luxembourg National Research Fund (FNR) & the National Centre for Research and Development (NCBR) under the SERENITY Project (ref. C22/IS/17395419; POLLUXXI/15/Serenity/2023)
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