Per-Modality Noise Scheduling in Multimodal Systems

• Per-modality noise scheduling is a strategy that adapts noise injection for each sensor or channel by balancing data freshness and precision.
• Algorithmic methods, including sliding window dynamic programming and neural schedulers, optimize performance under resource and variability constraints.
• Empirical studies in sensor networks and diffusion models demonstrate improved estimation accuracy and generative quality, evidenced by reduced error metrics and better FID scores.

Per-modality noise scheduling refers to the set of theory-driven, algorithmic, and architectural strategies by which models—particularly in domains such as sensor fusion, multimodal generative modeling, resource allocation, and robust distributed systems—adapt the injection, scheduling, or weighting of noise for each modality or channel as a function of their reliability, task relevance, or information contribution. This concept encompasses both classical signal-processing contexts (e.g., sensor networks or control systems) and modern machine learning, including diffusion models and large multimodal foundation models, where the "modality" may denote input type (image, text, audio) or information source (sensor, network channel).

1. Theoretical Underpinnings: Error Sensitivity to Freshness and Precision

The classical setting in wireless networked control systems exposes the fundamental nonlinear relationship between estimation error and the dual factors of observation freshness (data age, τ(t)) and precision (noise variance, σ²ₒ(t)). The closed-form derivation from (Ma et al., 2022) demonstrates that the expected state estimation error $J_E(T)$ can be quantified as: $$J_E(T) = \frac{1}{T} \sum_{t=0}^{T-1} \sum_{q=t}^{T} \prod_{n=1}^{q-t} \left[a^2 (1 - k(t+n))^2\right] \cdot f(t, \sigma^2_o(t), \tau_t)$$ where $f(\cdot)$ encapsulates process noise accumulation ($C_p$), observation noise effects ($C_s$), and historical error correlation ($C_e$). The system dynamics coefficient $a$ renders the error exponentially sensitive to both modalities’ age and precision.

This establishes the basis for modality-aware scheduling: modalities (sensors or channels) with intrinsically lower observation noise can tolerate increased staleness, whereas those with higher noise require more frequent updates to maintain aggregate system estimation optimality. In application, this may involve explicit scheduling policies that account for both channel delay and sensor noise profile.

2. Algorithmic Strategies for Modality-Aware Scheduling

Per-modality scheduling often formalizes as an optimization problem, e.g., in the LQG control case from (Ma et al., 2022), minimizing average squared estimation error subject to constraints on channel capacity and heterogeneous sensor characteristics. The computationally tractable solution via a sliding window algorithm leverages myopic N-step lookahead dynamic programming:

• State: Age vector of all modalities (sensors), possibly extended to historical age profiles
• BeLLMan recursion: Backward induction using conditional probabilities for sensor selection
• Policy: At each slot, select the modality yielding lowest expected future error, balancing freshness and noise variance.

In advanced distributed resource allocation, sign-based dynamics (Doostmohammadian et al., 2023) serve to filter out perturbations from noise, with the sign mapping acting as a robust filter across modalities. Optimizations are blended with control-theoretic Lyapunov stability and network science notions of uniform-connectivity to guarantee robustness.

For multimodal foundation models, dynamic scheduling mechanisms (e.g., DMS (Tanaka et al., 15 Jun 2025), MA-AFS (Bennett et al., 15 Jun 2025)) employ learnable neural schedulers that output per-modality fusion weights. Factors considered include confidence (entropy-based), uncertainty (Monte Carlo dropout variance), and cross-modal semantic alignment. The scheduling function fuses these scores, enabling dynamic weighting: $$\omega_m(x) = \frac{\exp(\alpha \cdot c_m(x) - \beta \cdot u_m(x) + \gamma \cdot s_m(x))}{\sum_j \exp(\alpha \cdot c_j(x) - \beta \cdot u_j(x) + \gamma \cdot s_j(x))}$$ These mechanisms allow real-time adaptation to instance-level noise and reliability.

3. Noise Schedule Design in Diffusion and Generative Models

In diffusion models, noise scheduling defines the progression of noise injected into the forward process, greatly affecting denoising performance and sample quality. Key advances include:

• Schedule Function Parameterizations: Employing linear, cosine, sigmoid, exponential, Laplace, Cauchy, Fibonacci, or monotonic neural network-based schedules (Chen, 2023, Guo et al., 7 Feb 2025, Hang et al., 3 Jul 2024). Each offers distinct trade-offs in smoothness, emphasis on mid-step noise, and ability to adapt to modality or task.
• Importance Sampling on logSNR: As introduced in (Hang et al., 3 Jul 2024), strategic sampling around the transition between signal and noise dominance (logSNR ≈ 0) accelerates training by focusing computational effort on the most informative noise levels. Probability density for λ = log SNR is adapted to concentrate samples in critical regions, with Laplace, Cauchy, and shifted-cosine schedules outperforming standard cosine.
• Scaling and Curriculum Frameworks: Input scaling shifts the effective logSNR (Λ_scaled(t) = Λ(t) + log b), enabling per-modality adaptation without full redesign of γ(t) (Chen, 2023). Polynomial scheduling with sinusoidal curriculum (Gokmen et al., 9 Apr 2024) guarantees consistency, smooth transitions, and tailored noise distributions, further improving denoising efficiency.
• Information-Theoretic Time Schedulers: Entropic and rescaled entropic time (Stancevic et al., 18 Apr 2025) reparameterize the diffusion timeline so that each step contributes equivalent mutual information, computed via conditional entropy H[x₀|x_t]. This approach, computationally tractable via training loss, ensures equal contribution of every (per-modality) sample to final generation.

4. Adaptation for Heterogeneous and Multimodal Systems

Modality-aware noise scheduling is essential in systems where input modalities vary in information content, redundancy, and signal-to-noise characteristics:

• Sensor Heterogeneity: In sensor networks (Ma et al., 2022), modalities such as visual, thermal, accelerometric, or magnetic sensors display disparate noise profiles. Plugging modality-specific σ²ₒ,m into scheduling functions enables optimal trade-off computation between precision and freshness.
• Multimodal Large Models: DMS (Tanaka et al., 15 Jun 2025) and MA-AFS (Bennett et al., 15 Jun 2025) frameworks compute per-sample and per-modality weights using confidence, uncertainty, and semantic consistency metrics. Lightweight neural schedulers predict adaptive fusion weights by integrating modality-level entropy and cross-modal agreement cues. Scheduling is differentiable, theoretically consistent, and does not increase model capacity.
• Diffusion over Modalities: For generative tasks involving multi-channel or multi-modal input (e.g., audio, video, image, text), per-modality schedules can employ customizable curriculum (polynomial or sinusoidal), learnable neural networks, and information-based criteria to optimize injection and removal of noise appropriate to modality-specific learning requirements.

5. Empirical Validation and Performance Metrics

Empirical analyses confirm the superiority and necessity of per-modality scheduling approaches across domains:

• Networked Control Performance: Simulation results (Ma et al., 2022) show that sliding window dynamic scheduling consistently outperforms age-minimal, variance-minimal, or random sensor selection, particularly when observation noise or delay increases.
• Generative Model Quality: In diffusion models, polynomial noise scheduling paired with sinusoidal curriculum (Gokmen et al., 9 Apr 2024) yields notable reductions in FID, outperforming log-normal schedules and abruptly discretized curricula (e.g., FID 33.54 → 30.48 on CIFAR-10).
• Diffusion Training Efficiency: Importance-sampled Laplace schedules (Hang et al., 3 Jul 2024) achieve better FID scores (e.g., Laplace: 7.96 vs. Cosine: 11.06 at CFG=3.0), with observed improvements across prediction targets (x₀, ε, velocity).
• Robustness and Generalization in Multimodal Models: DMS (Tanaka et al., 15 Jun 2025) improves VQA accuracy (+2.3%), Recall@1 (+3.1%), and is especially robust under corrupted modality conditions (performance retained: DMS 88.5% vs. Static 78.6%).
• Distributed Resource Allocation: Sign-based dynamics (Doostmohammadian et al., 2023) maintain resource-demand equality and constraint feasibility under varying noise, with theoretical guarantees of convergence to an ε-neighborhood of the optimum.

6. Design Principles, Limitations, and Future Directions

The field has established several principles for effective per-modality noise scheduling:

• Scheduling should jointly consider modality-specific noise levels, information redundancy, temporal coherence, and cross-modal alignment.
• Algorithms must be designed to adaptively integrate reliability metrics and entropy signals, especially under noise, missingness, or domain shifts.
• Learnable schedulers provide flexibility to tailor scheduling to data characteristics, but require careful hyperparameter tuning and robust theoretical analysis (e.g., bi-level optimization and convergence guarantees).
• Information-theoretic approaches (e.g., entropic time) invite further research in extending to discrete modalities, cross-modal fusion, and loss-driven schedule estimation.
• There remains open ground in integrating per-modality schedules into broader architectures (e.g., RIN (Chen, 2023), multi-agent systems, or large multimodal foundation models), particularly with respect to multi-scale signal characteristics and temporal dependencies.

7. Applications and Broader Implications

Per-modality noise scheduling is central to:

• Wireless and Sensor Networks: Dynamic scheduling for state estimation, control performance, and system robustness (Ma et al., 2022, Doostmohammadian et al., 2023).
• Diffusion-Based Generative AI: Quality and efficiency improvements in image, audio, and multimodal generation (Chen, 2023, Gokmen et al., 9 Apr 2024, Hang et al., 3 Jul 2024, Guo et al., 7 Feb 2025, Stancevic et al., 18 Apr 2025).
• Multimodal Foundation Models: Adaptive fusion for vision-language tasks (retrieval, captioning, VQA) (Tanaka et al., 15 Jun 2025, Bennett et al., 15 Jun 2025).
• Distributed Resource Allocation: Robust scheduling under fluctuating environmental noise and network conditions (Doostmohammadian et al., 2023).
• Future multimodal and cross-modal systems: Integration of per-modality scheduling principles—grounded in both statistical learning and control theory—will underpin the next generation of robust, uncertainty-aware, and scalable AI architectures.

Per-modality noise scheduling now constitutes a rigorous, empirically validated design principle across multiple application domains, distinguished by its ability to jointly optimize system-level performance, training convergence, and output quality by tailoring noise injection or weighting to the specific properties and reliability of each modality.