example_papers/dual_expert_denoiser/ideas.json

[
    {
        "Name": "learning_rate_schedule",
        "Title": "Adaptive Learning Rate Schedules: Comparing different learning rate schedules for diffusion models.",
        "Experiment": "In this experiment, we compare the performance of different learning rate schedules on diffusion model performance. We use the final estimated KL as the evaluation metric.",
        "Interestingness": 4,
        "Feasibility": 10,
        "Novelty": 3,
        "novel": true
    },
    {
        "Name": "comparative_embedding_study",
        "Title": "Comparative Study of Embedding Strategies for Low-Dimensional Diffusion Models",
        "Experiment": "Modify the MLPDenoiser class to support three embedding types: 1) original sinusoidal, 2) simple learnable (nn.Embedding), and 3) transformer-style positional encoding (learnable). Train models with each embedding type on all datasets. Compare performance using KL divergence, training time, and inference time. Analyze learned embeddings across datasets to understand adaptation to different distributions.",
        "Interestingness": 8,
        "Feasibility": 7,
        "Novelty": 7,
        "novel": true
    },
    {
        "Name": "parameterized_noise_schedule",
        "Title": "Parameterized Noise Schedules for Low-Dimensional Diffusion Models",
        "Experiment": "Modify the NoiseScheduler class to include a shape parameter in the beta schedule calculation. This parameter will allow for a continuous range of schedules between linear and highly nonlinear. Conduct a grid search over this parameter for each dataset, analyzing the impact on convergence speed, final KL divergence, and sample quality. Investigate correlations between optimal shape parameters and dataset characteristics.",
        "Interestingness": 8,
        "Feasibility": 9,
        "Novelty": 7,
        "novel": false
    },
    {
        "Name": "quadrant_conditional_diffusion",
        "Title": "Quadrant-Based Conditional Generation in Low-Dimensional Diffusion Models",
        "Experiment": "Modify MLPDenoiser to accept a 2-bit condition vector representing quadrants. Update the forward method to incorporate this condition. Adjust the training loop to include quadrant information for each sample. Modify the sampling process to accept quadrant conditions. Generate samples for each quadrant and evaluate the percentage of samples that fall in the intended quadrant. Compare the quality of generated samples, quadrant accuracy, and KL divergence across all datasets with and without conditioning.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 8,
        "novel": true
    },
    {
        "Name": "dual_expert_denoiser",
        "Title": "Dual-Expert Denoiser for Improved Mode Capture in Low-Dimensional Diffusion Models",
        "Experiment": "Modify MLPDenoiser to implement a dual-expert architecture. Create a simple gating network that outputs a single weight (sigmoid output) based on the noisy input and timestep. Implement two expert networks with the same structure as the original denoising network. Combine expert outputs using the gating weight. Train models with both the original and new architecture on all datasets, with particular focus on 'moons' and 'dino'. Compare performance using KL divergence, sample diversity metrics (e.g., number of modes captured), and visual inspection of generated samples. Analyze the specialization of experts across different regions of the data distribution.",
        "Interestingness": 8,
        "Feasibility": 8,
        "Novelty": 8,
        "novel": true
    },
    {
        "Name": "adaptive_dual_scale_denoising",
        "Title": "Adaptive Dual-Scale Denoising for Dynamic Feature Balancing in Low-Dimensional Diffusion Models",
        "Experiment": "Modify MLPDenoiser to implement a dual-scale processing approach with two parallel branches: a global branch for the original input and a local branch for an upscaled input. Introduce a learnable, timestep-conditioned weighting factor to dynamically balance the contributions of global and local branches. Train models with both the original and new architecture on all datasets. Compare performance using KL divergence and visual inspection of generated samples. Analyze how the weighting factor evolves during the denoising process and its impact on capturing global structure vs. local details across different datasets and timesteps.",
        "Interestingness": 9,
        "Feasibility": 8,
        "Novelty": 8,
        "novel": true
    },
    {
        "Name": "diffusion_trajectory_analysis",
        "Title": "Analyzing Data Understanding Through Diffusion Trajectories in Low-Dimensional Space",
        "Experiment": "1. Modify MLPDenoiser to output both denoised sample and predictions of original data properties (e.g., quadrant, distance from origin). 2. Adjust the loss function to include both denoising and property prediction losses. 3. Implement a simple metric to quantify prediction accuracy at different timesteps. 4. Train the modified model on all datasets. 5. Analyze how prediction accuracy changes across diffusion timesteps for different datasets and properties. 6. Compare final sample quality and KL divergence with the original model to ensure the additional task doesn't degrade performance.",
        "Interestingness": 8,
        "Feasibility": 9,
        "Novelty": 7,
        "novel": true
    },
    {
        "Name": "transfer_learning_diffusion",
        "Title": "Transfer Learning for Efficient Adaptation of Low-Dimensional Diffusion Models",
        "Experiment": "1. Train a base MLPDenoiser on three datasets (circle, line, moons). 2. Implement a fine-tuning procedure with early stopping based on validation loss. 3. For the held-out dataset (dino), perform fine-tuning with varying amounts of data (10%, 25%, 50%, 100%) and record the number of steps to convergence. 4. Compare KL divergence, sample quality, and preservation of specific dataset characteristics (e.g., modality, symmetry) of the fine-tuned model against a model trained from scratch on the full dino dataset. 5. Analyze the learned features of the base model and how they adapt during fine-tuning. 6. Repeat the experiment with different combinations of source and target datasets to assess generalization.",
        "Interestingness": 8,
        "Feasibility": 9,
        "Novelty": 7,
        "novel": true
    },
    {
        "Name": "activation_space_analysis",
        "Title": "Unveiling Learned Representations in Low-Dimensional Diffusion Models via Activation Space Analysis",
        "Experiment": "1. Modify MLPDenoiser to allow extraction of internal activations from different layers. 2. Implement activation visualization tools (e.g., t-SNE, UMAP) for different timesteps and layers. 3. Train models on all datasets and collect activations at various timesteps during inference. 4. Analyze how activations evolve across timesteps, differ between datasets, and vary between layers. 5. Investigate correlations between activation patterns and sample quality/KL divergence. 6. Compare activation spaces between datasets to identify shared and unique features learned by the model.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 8,
        "novel": true
    },
    {
        "Name": "curriculum_diffusion_learning",
        "Title": "Curriculum Learning via Progressive Diffusion Steps in Low-Dimensional Diffusion Models",
        "Experiment": "1. Modify NoiseScheduler to support a variable number of maximum timesteps. 2. Implement a simple curriculum that linearly increases the maximum number of diffusion steps during training. 3. Adjust the training loop to use the current maximum timestep when sampling. 4. Train models using both standard and curriculum approaches on all datasets. 5. Compare convergence speed, final KL divergence, and sample quality. 6. Evaluate sample quality at fixed intervals (e.g., every 1000 steps) during training for both approaches. 7. Analyze how curriculum learning affects the model's denoising ability at different noise levels throughout training.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 8,
        "novel": true
    },
    {
        "Name": "input_perturbation_robustness",
        "Title": "Analyzing and Improving Robustness to Input Perturbations in Low-Dimensional Diffusion Models",
        "Experiment": "1. Implement FGSM-like perturbations on input data with varying epsilon values. 2. Modify the training loop to include perturbed examples (50% clean, 50% perturbed). 3. Train models with both standard and perturbation-aware training on all datasets. 4. Evaluate robustness by measuring KL divergence and Frechet distance between real and generated samples under different perturbation strengths. 5. Visualize the diffusion trajectories of clean and perturbed samples in 2D space. 6. Analyze how perturbation-aware training affects the model's performance on clean data and its ability to denoise perturbed inputs.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 8,
        "novel": true
    },
    {
        "Name": "cycle_consistent_diffusion",
        "Title": "Cycle-Consistent Diffusion: Enhancing Reversibility in Low-Dimensional Diffusion Models",
        "Experiment": "1. Modify MLPDenoiser to output both denoised and re-noised samples, using the reverse noise schedule for re-noising. 2. Implement a cycle consistency loss measuring the MSE between original noisy inputs and re-noised samples. 3. Adjust the training loop to incorporate the new loss term, balancing it with the original denoising loss. 4. Train models with both standard and cycle-consistent approaches on all datasets. 5. Compare convergence speed, final KL divergence, sample quality, and a new cycle consistency metric. 6. Analyze how cycle consistency affects the model's performance across different noise levels and timesteps. 7. Visualize the reversibility of the diffusion process by plotting trajectories of samples through denoising and re-noising. 8. Compare learned noise distributions between standard and cycle-consistent models.",
        "Interestingness": 9,
        "Feasibility": 7,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "score_based_diffusion",
        "Title": "Score-Based Diffusion: Implicit Energy Learning in Low-Dimensional Diffusion Models",
        "Experiment": "1. Modify MLPDenoiser to output the score (gradient of log-density) instead of noise. 2. Implement a score-matching loss function (e.g., denoising score matching). 3. Adjust the training loop to use the new loss function. 4. Train models with both standard and score-based approaches on all datasets. 5. Compare KL divergence and sample quality between the two approaches. 6. Visualize the learned score field and diffusion trajectories in 2D space for each dataset. 7. Analyze how the learned score field captures the structure of different data distributions. 8. Investigate the relationship between the score field and the noise prediction in the original model.",
        "Interestingness": 9,
        "Feasibility": 8,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "diffusion_augmented_density_estimation",
        "Title": "Enhancing Density Estimation through Diffusion-based Data Augmentation in Low-Dimensional Spaces",
        "Experiment": "1. Generate sample sets (e.g., 50,000) for each dataset using the trained diffusion model at various timesteps. 2. Implement two density estimators: kernel density estimation (KDE) and a small neural network. 3. Train these estimators on: a) original data only, b) diffusion-generated samples from different timesteps, c) mixed original and generated data. 4. Evaluate using log-likelihood on held-out test set and Maximum Mean Discrepancy (MMD) between estimated and true distributions. 5. Analyze how diffusion timestep affects augmentation quality and density estimation performance. 6. Compare the best diffusion-augmented model against traditional methods in a simple anomaly detection task. 7. Discuss implications for using diffusion models as data augmentation tools in density estimation, especially in low-data regimes.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "temporal_feature_importance",
        "Title": "Temporal Dynamics of Feature Importance in Low-Dimensional Diffusion Models",
        "Experiment": "1. Modify MLPDenoiser to compute feature importance scores using input occlusion. 2. Adapt the training loop to collect feature importance scores at different timesteps. 3. Implement 2D heatmap visualizations to display feature importance over time for each dataset. 4. Train models on all datasets and collect feature importance data during inference. 5. Analyze how feature importance evolves across timesteps and differs between datasets. 6. Compare feature importance patterns between high-quality and low-quality generated samples. 7. Investigate correlations between feature importance dynamics and final sample quality/KL divergence.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "auxiliary_latent_diffusion",
        "Title": "Auxiliary Latent Dimension for Interpretable Low-Dimensional Diffusion",
        "Experiment": "1. Modify MLPDenoiser to output an additional scalar value alongside the 2D prediction. 2. Implement an auxiliary loss to encourage this latent value to capture meaningful data properties (e.g., distance from origin). 3. Adjust the training loop to include the new auxiliary loss term. 4. Train models with both standard and auxiliary latent approaches on all datasets. 5. Compare KL divergence and sample quality between the two approaches. 6. Visualize how the learned latent dimension correlates with data properties for each dataset. 7. Analyze how the latent dimension evolves during the diffusion process and its impact on sample quality. 8. Investigate if the auxiliary latent dimension improves the model's ability to capture specific dataset characteristics.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 8,
        "novel": true
    },
    {
        "Name": "manifold_preserving_diffusion",
        "Title": "Manifold-Preserving Diffusion: Local Structure Regularization in Low-Dimensional Spaces",
        "Experiment": "1. Implement a function to compute pairwise distances within mini-batches. 2. Modify the loss function to include a regularization term that encourages preservation of these pairwise distances during denoising. 3. Adjust the training loop to incorporate the new loss term, balancing it with the original denoising loss. 4. Train models with both standard and manifold-preserving approaches on all datasets. 5. Compare KL divergence, sample quality, and a new metric measuring preservation of local structure. 6. Visualize diffusion trajectories and how they maintain local relationships for each dataset. 7. Analyze how structure preservation varies across different noise levels and timesteps. 8. Discuss potential extensions to higher-dimensional spaces.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "energy_guided_diffusion",
        "Title": "Energy-Guided Diffusion: Incorporating Learned Energy Functions in Low-Dimensional Diffusion Models",
        "Experiment": "1. Implement a simple energy network (e.g., 2-layer MLP) that outputs a scalar energy value. 2. Modify MLPDenoiser to accept energy information as additional input. 3. Implement an energy-based loss function to train the energy network. 4. Adjust training loop to alternate between diffusion model and energy network updates. 5. Train energy-guided models on all datasets and compare against standard diffusion models. 6. Analyze sample quality, KL divergence, training dynamics, and computational efficiency. 7. Visualize learned energy landscapes for each dataset. 8. Investigate how energy guidance affects the diffusion process at different timesteps.",
        "Interestingness": 9,
        "Feasibility": 8,
        "Novelty": 8,
        "novel": false
    },
    {
        "Name": "critical_point_analysis",
        "Title": "Critical Point Analysis: Quantifying Key Moments in Low-Dimensional Diffusion Trajectories",
        "Experiment": "1. Modify the sampling process to store model predictions at each timestep. 2. Implement a function to identify 'critical points' using statistical measures (e.g., z-score of prediction changes). 3. Visualize diffusion trajectories with highlighted critical points for each dataset. 4. Quantify critical points by counting their occurrence and measuring average magnitude of changes. 5. Perform comparative analysis of critical point patterns across datasets. 6. Investigate correlations between critical point metrics and final sample quality/KL divergence. 7. Analyze how critical points relate to dataset characteristics (e.g., modality, symmetry). 8. Experiment with using critical point information to guide adaptive sampling or model architecture improvements.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "geometric_flow_analysis",
        "Title": "Geometric Flow Analysis: Visualizing Manifold Learning in Low-Dimensional Diffusion Models",
        "Experiment": "1. Implement functions to estimate local density and directional flow of point clouds. 2. Modify the sampling process to compute these geometric properties at key denoising steps. 3. Create heat maps and vector field visualizations to display density and flow evolution during denoising. 4. Develop metrics to quantify changes in geometric properties across denoising steps. 5. Compare geometric flow patterns across different datasets and noise schedules. 6. Analyze correlations between geometric flow metrics and final sample quality/KL divergence. 7. Visualize how different model architectures affect the geometric flow patterns. 8. Discuss implications of findings for understanding and improving higher-dimensional diffusion models.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "dual_resolution_diffusion",
        "Title": "Dual-Resolution Diffusion: Enhancing Global-Local Structure Learning in Low-Dimensional Spaces",
        "Experiment": "1. Modify MLPDenoiser to create a dual-resolution architecture with coarse and fine levels. 2. Implement simple downsampling (average pooling) and upsampling (nearest neighbor) operations for 2D data. 3. Adjust the forward pass to first process downsampled data, then use the coarse prediction to inform the fine-level processing. 4. Modify the loss function to include weighted contributions from both resolution levels. 5. Adapt the sampling process to use the dual-resolution approach. 6. Train models with both standard and dual-resolution approaches on all datasets. 7. Compare KL divergence, sample quality, and convergence speed. 8. Introduce a new metric to measure global structure preservation. 9. Analyze computational overhead and trade-offs between model complexity and performance gains.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 8,
        "novel": true
    },
    {
        "Name": "connected_component_tracking",
        "Title": "Tracking Connected Components in Low-Dimensional Diffusion Models",
        "Experiment": "1. Implement a function to identify connected components using a simple clustering algorithm (e.g., DBSCAN). 2. Modify the sampling process to track the number and sizes of connected components at each denoising step. 3. Create visualizations showing the evolution of connected components during denoising. 4. Implement metrics to quantify changes in component structure (e.g., Jaccard index between consecutive steps). 5. Train models on all datasets and collect component data during inference. 6. Analyze how component structure evolves across timesteps and differs between datasets. 7. Compare the final component structure of generated samples with that of the original data distribution. 8. Investigate correlations between component evolution patterns and final sample quality/KL divergence. 9. Compare component evolution across different noise schedules and model architectures.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 8,
        "novel": true
    },
    {
        "Name": "adaptive_disentangled_diffusion",
        "Title": "Adaptive Disentangled Diffusion: Learning Separable Representations in Low-Dimensional Diffusion Models",
        "Experiment": "1. Modify MLPDenoiser to include a learnable affine transformation before coordinate conversion. 2. Implement a differentiable coordinate transformation layer supporting both Cartesian and polar representations. 3. Adjust the loss function to include separate terms for each component and a disentanglement regularization term based on mutual information. 4. Modify the sampling process to use the disentangled predictions. 5. Train models with standard, polar-coordinate, and disentangled approaches on all datasets. 6. Implement visualization tools to display separated components during the diffusion process. 7. Analyze how disentanglement affects sample quality, KL divergence, and interpretability using the mutual information metric. 8. Compare the learned disentangled representations across different datasets and investigate their generalization properties. 9. Discuss potential extensions to higher-dimensional spaces and other coordinate systems.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "multi_modal_diffusion",
        "Title": "Multi-Modal Diffusion: Learning and Generating from Multiple 2D Distributions Simultaneously",
        "Experiment": "1. Modify MLPDenoiser to accept a 4-bit one-hot encoded dataset identifier (circle, dino, line, moons) as additional input. 2. Adjust the training loop to sample equally from all four datasets in each batch. 3. Implement a conditional sampling procedure that generates samples for a specified dataset. 4. Train the multi-modal model on all datasets simultaneously. 5. Evaluate performance using KL divergence, visual inspection, and a new 'distribution accuracy' metric (percentage of generated samples matching the intended distribution). 6. Compare against individual models trained on each dataset, analyzing differences in model capacity and training dynamics. 7. Investigate cross-dataset influences by generating samples with mismatched dataset identifiers. 8. Analyze the model's internal representations to understand how it separates different distributions. 9. Discuss potential applications in domain adaptation and multi-task learning for diffusion models.",
        "Interestingness": 9,
        "Feasibility": 8,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "linear_diffusion_steering",
        "Title": "Linear Diffusion Steering: Controlled Generation via Trajectory Guidance in Low-Dimensional Diffusion Models",
        "Experiment": "1. Implement a linear path definition function in 2D space. 2. Modify NoiseScheduler to include a linear guidance term with adjustable strength. 3. Adapt the sampling process to use the guided scheduler. 4. Train models on all datasets using the original method. 5. Generate samples using both standard and guided approaches with varying guidance strengths. 6. Visualize diffusion trajectories and final samples. 7. Measure path adherence using mean squared distance from the defined path. 8. Compare sample quality (KL divergence) and path adherence across guidance strengths. 9. Analyze the trade-off between following the defined path and maintaining data distribution characteristics.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "diffusion_decision_boundary",
        "Title": "Diffusion Decision Boundary Analysis: Visualizing and Optimizing Denoising Directions in Low-Dimensional Diffusion Models",
        "Experiment": "1. Modify MLPDenoiser to output both the denoised prediction and the raw network output before any activation. 2. Implement a grid-based sampling method to evaluate model predictions across the 2D space. 3. Create visualization tools to display vector fields of denoising directions and magnitude. 4. Implement metrics to quantify decision boundary characteristics (e.g., curvature, consistency). 5. Analyze decision boundaries at different timesteps and training stages for all datasets. 6. Compare decision boundaries between high-quality and low-quality samples, and across different model architectures. 7. Investigate correlations between decision boundary metrics and final sample quality/KL divergence. 8. Use decision boundary analysis to detect and mitigate mode collapse. 9. Experiment with using decision boundary information to guide model improvements or sampling strategies.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "adaptive_temporal_consistency",
        "Title": "Adaptive Temporal Consistency Learning in Low-Dimensional Diffusion Models",
        "Experiment": "1. Modify MLPDenoiser to store the previous timestep's noise prediction. 2. Implement an adaptive temporal consistency loss that measures the discrepancy between the current and previous noise predictions, with higher weight at earlier timesteps. 3. Adjust the training loop to compute this additional loss and balance it with the original denoising loss. 4. Train models with both standard and adaptive temporal consistency approaches on all datasets. 5. Compare KL divergence, sample quality, and convergence speed between the two approaches. 6. Analyze how temporal consistency and its impact vary across different noise levels. 7. Visualize the learned noise predictions at adjacent timesteps to understand the model's temporal understanding. 8. Investigate if this approach improves the model's ability to capture long-range dependencies in the data.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 8,
        "novel": true
    },
    {
        "Name": "topological_feature_evolution",
        "Title": "Topological Feature Evolution in Low-Dimensional Diffusion Trajectories",
        "Experiment": "1. Implement functions to compute simple topological features: number of connected components and number of holes (loops) using scipy.ndimage, with a preliminary density estimation step using gaussian_kde. 2. Modify the sampling process to compute these topological features at key denoising steps. 3. Create visualizations showing the evolution of these features during the diffusion process. 4. Develop metrics to quantify changes in topological features across denoising steps. 5. Train models on all datasets and collect topological data during inference. 6. Analyze how topological features evolve across timesteps and differ between datasets. 7. Investigate correlations between topological feature evolution and final sample quality/KL divergence. 8. Compare topological evolution patterns across different noise schedules and model architectures. 9. Discuss implications for understanding and improving diffusion models in capturing and preserving topological structures.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "data_complexity_evolution",
        "Title": "Tracking Data Complexity Evolution in Low-Dimensional Diffusion Models",
        "Experiment": "1. Implement a simple grid-based local PCA method to estimate data complexity. 2. Modify the sampling process to compute complexity estimates at regular intervals during denoising. 3. Create visualizations showing the evolution of data complexity during the diffusion process. 4. Analyze how complexity evolves across timesteps and differs between datasets. 5. Investigate correlations between complexity evolution patterns and final sample quality/KL divergence. 6. Implement a dynamic timestep adjustment method based on complexity changes. 7. Compare the performance and efficiency of complexity-guided diffusion against the standard fixed-timestep approach across all datasets.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "intrinsic_dimensionality_tracking",
        "Title": "Leveraging Intrinsic Dimensionality Evolution for Improved Low-Dimensional Diffusion Models",
        "Experiment": "1. Implement an efficient correlation dimension estimator for local intrinsic dimensionality. 2. Modify the sampling process to compute intrinsic dimensionality estimates at key intervals during denoising. 3. Create visualizations showing the evolution of intrinsic dimensionality during the diffusion process. 4. Analyze how intrinsic dimensionality evolves across timesteps and differs between datasets. 5. Compare the final intrinsic dimensionality of generated samples with the original data distribution. 6. Investigate correlations between intrinsic dimensionality evolution patterns and sample quality/KL divergence. 7. Experiment with adaptive noise schedules based on intrinsic dimensionality changes. 8. Use intrinsic dimensionality tracking to detect and address mode collapse.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "uncertainty_quantification_diffusion",
        "Title": "Uncertainty Quantification and Visualization in Low-Dimensional Diffusion Models",
        "Experiment": "1. Modify MLPDenoiser to output mean and log-variance for each dimension. 2. Implement a negative log-likelihood loss function based on Gaussian distribution. 3. Create visualization tools for uncertainty heatmaps and diffusion trajectories with uncertainty. 4. Train models on all datasets using the new uncertainty-aware loss. 5. Generate uncertainty visualizations at different denoising steps for all datasets. 6. Analyze how uncertainty evolves across timesteps and relates to the original data distribution. 7. Compare uncertainty estimates with actual denoising errors to assess model calibration. 8. Investigate correlations between uncertainty patterns and final sample quality/KL divergence. 9. Experiment with uncertainty-guided sampling by prioritizing high-uncertainty regions during the denoising process. 10. Compare uncertainty patterns across different model architectures and noise schedules.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 8,
        "novel": true
    },
    {
        "Name": "diffusion_enhanced_tsne",
        "Title": "Enhancing t-SNE with Diffusion Model Representations for Improved Data Visualization",
        "Experiment": "1. Use scikit-learn's t-SNE implementation. 2. Modify MLPDenoiser to output intermediate representations at each residual block. 3. Train diffusion models on all datasets. 4. For each dataset, apply t-SNE to: (a) raw data, (b) final diffusion representations, (c) representations at different diffusion timesteps. 5. Implement metrics to compare quality of embeddings (e.g., trustworthiness, continuity). 6. Visualize how embeddings evolve across diffusion timesteps. 7. Analyze preservation of local and global structures in diffusion-enhanced t-SNE embeddings. 8. Explore applications in data augmentation and anomaly detection using the hybrid approach. 9. Compare computational efficiency and embedding quality of standard t-SNE vs. diffusion-enhanced version.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "symmetry_guided_diffusion",
        "Title": "Symmetry-Guided Diffusion: Enhancing Low-Dimensional Generative Models with Geometric Priors",
        "Experiment": "1. Implement a function to compute reflectional symmetry scores across the y-axis for 2D data points. 2. Modify MLPDenoiser to accept a scalar symmetry score as additional input. 3. Implement a symmetry guidance term in the loss function that encourages maintaining the input symmetry score during denoising. 4. Adjust the training loop to compute symmetry scores and incorporate the new loss term. 5. Train models with both standard and symmetry-guided approaches on all datasets. 6. Compare KL divergence, sample quality, and symmetry preservation using mean absolute difference between input and output symmetry scores. 7. Visualize diffusion trajectories and analyze how symmetry guidance affects the denoising process, especially for 'circle' and 'moons' datasets. 8. Investigate potential improvements in convergence speed and sample quality. 9. Discuss implications for extending this approach to other geometric priors and higher-dimensional spaces.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "pca_aligned_diffusion",
        "Title": "PCA-Aligned Diffusion: Enhancing Interpretability and Control in Low-Dimensional Generative Models",
        "Experiment": "1. Implement a function to compute PCA on each dataset, obtaining principal components and explained variance ratios. 2. Modify NoiseScheduler to work in PCA-aligned coordinates. 3. Adjust MLPDenoiser to operate in and output PCA-aligned coordinates. 4. Train models using both standard and PCA-aligned approaches on all datasets. 5. Compare KL divergence and sample quality between the two approaches. 6. Visualize diffusion trajectories in both original and PCA-aligned spaces. 7. Analyze how PCA alignment affects the interpretability of the diffusion process. 8. Experiment with controlled generation by manipulating noise along principal component directions. 9. Investigate potential improvements in convergence speed and sample diversity.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 8,
        "novel": true
    },
    {
        "Name": "grid_based_noise_adaptation",
        "Title": "Grid-Based Noise Adaptation for Enhanced Low-Dimensional Diffusion Models",
        "Experiment": "1. Modify NoiseScheduler to support grid-based noise level adjustments. 2. Implement a simple grid structure (e.g., 10x10) to store learnable noise adjustment factors. 3. Adjust MLPDenoiser to incorporate the grid-based noise level in its computations. 4. Modify the training loop to include the grid parameters in the optimization process. 5. Adapt the sampling process to use the grid-based noise levels during inference. 6. Train models with both standard and grid-based noise adaptation approaches on all datasets. 7. Compare KL divergence, sample quality, and convergence speed between the two approaches. 8. Introduce a 'noise adaptation effectiveness' metric by measuring the variance of learned grid values. 9. Visualize the learned noise adjustment grid at different timesteps. 10. Analyze computational overhead and discuss trade-offs between model complexity and performance gains.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "entropy_flow_analysis",
        "Title": "Entropy Flow Analysis in Low-Dimensional Diffusion Models",
        "Experiment": "1. Implement a function to estimate entropy using the existing npeet.entropy_estimators module. 2. Modify NoiseScheduler to compute and store entropy estimates at each timestep during forward diffusion. 3. Adapt the sampling process in experiment.py to compute entropy estimates during reverse diffusion. 4. Create visualizations showing the evolution of entropy during forward and reverse diffusion processes. 5. Analyze how entropy flow patterns differ between datasets and correlate with final sample quality/KL divergence. 6. Implement an adaptive noise schedule based on entropy change rates. 7. Compare model performance and sample quality between standard and entropy-guided diffusion processes across all datasets.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "curvature_aware_diffusion",
        "Title": "Curvature-Aware Diffusion: Leveraging Manifold Geometry for Enhanced Low-Dimensional Generative Models",
        "Experiment": "1. Implement a function to estimate local curvature in 2D using circle fitting on nearby points. 2. Modify the sampling process to compute and store curvature estimates at key denoising steps. 3. Create visualizations showing the evolution of local curvature alongside the diffusion process. 4. Analyze how curvature evolves across timesteps and differs between datasets. 5. Implement a curvature-guided sampling method that allocates more samples to high-curvature regions during inference. 6. Train models using the standard approach on all datasets. 7. Compare KL divergence and sample quality between standard and curvature-guided sampling. 8. Investigate correlations between curvature evolution patterns and final sample quality. 9. Discuss the trade-off between improved sample quality and computational overhead of curvature estimation.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "dual_scale_diffusion",
        "Title": "Dual-Scale Diffusion: Enhancing Low-Dimensional Generative Models with Coarse and Fine Noise Processing",
        "Experiment": "1. Modify NoiseScheduler to support two scales of noise (coarse and fine). 2. Adjust MLPDenoiser to process and output dual-scale noise predictions. 3. Implement a simple weighted sum function to combine coarse and fine noise predictions. 4. Adapt the training loop to compute losses for each scale and a combined loss. 5. Modify the sampling process to use dual-scale noise during inference. 6. Train models with both standard and dual-scale approaches on all datasets. 7. Compare KL divergence, sample quality, and convergence speed between the two approaches. 8. Implement a scale effectiveness metric by comparing the relative contributions of coarse and fine predictions to the final output. 9. Visualize the diffusion process at both scales using 2D heatmaps to show how coarse and fine noise patterns evolve. 10. Analyze computational overhead and discuss trade-offs between model complexity and performance gains.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "adaptive_multi_scale_diffusion",
        "Title": "Adaptive Multi-Scale Diffusion: Scale-Aware Learning in Low-Dimensional Generative Models",
        "Experiment": "1. Modify MLPDenoiser to process inputs at three fixed scales (original, 0.5x, and 2x) using learnable scale weights. 2. Implement a simple multi-scale input transformation function. 3. Adjust the training loop to compute losses at each scale and a combined loss. 4. Modify the sampling process to use multi-scale denoising during inference. 5. Train models with both standard and multi-scale approaches on all datasets. 6. Compare KL divergence, sample quality, and convergence speed between the two approaches, with particular focus on improvements for multi-scale datasets like 'dino'. 7. Implement a scale importance metric to track the contribution of each scale throughout the diffusion process. 8. Create stacked area charts to visualize the evolution of scale weights during training and sampling. 9. Analyze how different datasets utilize various scales and discuss implications for understanding data complexity.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "semantic_latent_interpolation",
        "Title": "Semantic Latent Space Interpolation in Low-Dimensional Diffusion Models",
        "Experiment": "1. Identify key semantic directions (rotation, scale) in the 2D latent space. 2. Modify the sampling process to allow controlled generation along these directions. 3. Create vector field visualizations showing the influence of semantic directions on generation. 4. Implement quantitative measures for control effectiveness (e.g., accuracy of rotation angle control). 5. Visualize interpolations in 2D space for each dataset. 6. Compare controlled generation results with original diffusion process. 7. Analyze how semantic directions vary across different datasets. 8. Discuss potential extensions to higher-dimensional spaces.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "moment_guided_diffusion",
        "Title": "Moment-Guided Diffusion: Enhancing Interpretability and Control in Low-Dimensional Generative Models",
        "Experiment": "1. Implement functions to compute mean and variance for 2D data. 2. Modify NoiseScheduler to compute and store these moments at each timestep during forward diffusion. 3. Adapt the sampling process to compute moments during reverse diffusion. 4. Create 2D visualizations showing the evolution of moments during forward and reverse diffusion processes. 5. Implement a moment-guided sampling method that slows down diffusion when moment discrepancies are high. 6. Train models using both standard and moment-guided approaches on all datasets. 7. Compare KL divergence, sample quality, and moment preservation between the two approaches. 8. Analyze how datasets with different moment characteristics (e.g., 'circle' vs 'moons') behave during diffusion. 9. Investigate potential improvements in interpretability, convergence speed, and sample quality.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "adaptive_local_complexity_diffusion",
        "Title": "Adaptive Local Complexity Diffusion: Dynamic Denoising for Varying Data Structures",
        "Experiment": "1. Implement a simple local complexity estimation function using local density estimation. 2. Modify NoiseScheduler to adjust step size based on local complexity. 3. Adapt the sampling process to use the complexity-aware denoising. 4. Train standard models on all datasets. 5. Compare standard and adaptive sampling approaches using KL divergence, sample quality, and generation speed. 6. Introduce a 'Complexity Adaptation Efficiency' metric to measure the method's effectiveness. 7. Visualize complexity estimates and their impact on the diffusion process for each dataset.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "attractor_analysis_manipulation",
        "Title": "Attractor Analysis and Manipulation in Low-Dimensional Diffusion Models",
        "Experiment": "1. Implement functions to identify fixed points and limit cycles in the 2D diffusion process. 2. Modify the sampling process to track and store attractor-related information during denoising. 3. Create vector field plots to visualize attractor dynamics and their evolution during the diffusion process. 4. Implement metrics to quantify attractor strength and sample diversity. 5. Develop a method to bias the sampling process towards or away from identified attractors using a simple additive term. 6. Train models on all datasets using the standard approach. 7. Compare sample quality (using KL divergence), diversity (using pairwise distances), and controllability (using distance to target attractor) between standard sampling and attractor-manipulated sampling. 8. Analyze how attractor dynamics differ across datasets and correlate with final sample quality. 9. Investigate the potential for using attractor manipulation to enhance multi-modal generation, especially for datasets like 'moons' and 'dino'.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "pdf_guided_diffusion",
        "Title": "PDF-Guided Diffusion: Leveraging Probability Density Estimation for Enhanced Low-Dimensional Generative Models",
        "Experiment": "1. Modify MLPDenoiser to output both denoised coordinates and log-probability density estimate. 2. Implement a simple histogram-based density estimation for ground truth. 3. Adjust training loop to incorporate density estimation loss. 4. Modify sampling process to bias towards higher-density regions using estimated densities. 5. Implement visualizations of estimated density fields and their difference from true density at different timesteps. 6. Train models on all datasets using both standard and PDF-guided approaches. 7. Compare KL divergence, sample quality, and introduce Jensen-Shannon divergence to evaluate density estimation accuracy. 8. Analyze how density estimates evolve during the diffusion process. 9. Experiment with using density estimates to detect and mitigate mode collapse.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "temporal_sensitivity_analysis",
        "Title": "Temporal Sensitivity Analysis: Unraveling the Memory of Diffusion Models",
        "Experiment": "1. Modify the sampling process to introduce controlled perturbations at specific timesteps. 2. Implement a function to measure the effect of perturbations on final samples using MSE. 3. Use importance sampling to efficiently explore the timestep-perturbation space. 4. Generate and visualize sensitivity profiles for each dataset using heatmaps. 5. Identify 'critical timesteps' where the model is most sensitive to perturbations. 6. Analyze correlations between sensitivity profiles and sample quality/KL divergence. 7. Experiment with allocating more compute resources to critical timesteps during sampling. 8. Investigate how sensitivity analysis can inform model architecture improvements.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "information_bottleneck_analysis",
        "Title": "Information Bottleneck Analysis in Low-Dimensional Diffusion Models",
        "Experiment": "1. Implement functions to estimate mutual information using npeet.entropy_estimators. 2. Modify NoiseScheduler to compute mutual information between: (a) original data and noisy versions, (b) consecutive timesteps, at regular intervals during forward diffusion. 3. Adapt the sampling process to compute these mutual information estimates during reverse diffusion. 4. Create visualizations showing the evolution of mutual information and identify potential information bottlenecks. 5. Analyze how information flow patterns and bottlenecks differ between datasets and correlate with sample quality. 6. Implement an adaptive noise schedule that slows down diffusion at identified bottlenecks. 7. Compare model performance between standard and bottleneck-aware diffusion processes. 8. Investigate how bottleneck analysis can inform model architecture improvements, such as adding skip connections at critical points.",
        "Interestingness": 9,
        "Feasibility": 8,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "manifold_navigation_analysis",
        "Title": "Manifold Navigation Analysis: Quantifying Diffusion Model's Adherence to Data Geometry",
        "Experiment": "1. Implement a grid-based approximation of the data manifold using local PCA on grid cells. 2. Modify the sampling process to track denoising trajectories and compute their alignment with the approximated manifold. 3. Implement a 'manifold adherence score' as the cosine similarity between denoising steps and local tangent spaces. 4. Create heatmap visualizations of manifold adherence scores across the 2D space at different timesteps. 5. Generate trajectory plots showing how samples move through the manifold-approximated space during denoising. 6. Analyze how manifold adherence patterns differ across datasets and correlate with final sample quality (KL divergence). 7. Compare manifold adherence scores at different stages of model training to visualize how the model's understanding of the manifold evolves. 8. Discuss potential extensions to higher-dimensional spaces and connections to traditional manifold learning techniques.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "optimal_transport_diffusion",
        "Title": "Optimal Transport Analysis for Enhanced Diffusion Processes",
        "Experiment": "1. Implement a function to estimate 2D Wasserstein distance using numpy (e.g., Earth Mover's Distance approximation). 2. Modify NoiseScheduler to compute and store Wasserstein distances during forward and reverse diffusion. 3. Create visualizations of Wasserstein distance evolution during diffusion processes. 4. Implement a Wasserstein-guided sampling method that adjusts step sizes inversely proportional to the rate of change in Wasserstein distance. 5. Train models using both standard and Wasserstein-guided approaches on all datasets. 6. Compare KL divergence, sample quality, and introduce a 'Transport Efficiency' metric (total Wasserstein distance reduction / number of steps). 7. Analyze correlations between Wasserstein distance patterns and final sample quality across datasets.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "iterative_diffusion_augmentation",
        "Title": "Iterative Diffusion Augmentation: Self-Improving Low-Dimensional Generative Models",
        "Experiment": "1. Implement a 'sample pool' to store generated samples. 2. Modify the training loop to alternate between training on real data and the sample pool. 3. After each epoch, generate new samples and update the sample pool based on log-likelihood. 4. Implement metrics for distribution coverage (e.g., k-means clustering) and sample diversity (e.g., pairwise distances). 5. Track KL divergence, sample quality, distribution coverage, and sample diversity across iterations. 6. Implement early stopping based on KL divergence improvement. 7. Compare final model performance with and without iterative augmentation across all four datasets. 8. Analyze how the ratio of real to generated samples in training affects performance. 9. Visualize the evolution of the sample pool across iterations.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "intrinsic_dimensionality_diffusion",
        "Title": "Analyzing Intrinsic Dimensionality Evolution in Low-Dimensional Diffusion Models",
        "Experiment": "1. Implement a function to estimate local intrinsic dimensionality (LID) as a binary classification (1D vs 2D) using local PCA. 2. Modify both forward and reverse diffusion processes to compute LID estimates at regular intervals. 3. Create side-by-side heatmap visualizations showing LID evolution during forward and reverse diffusion. 4. Generate time series plots of LID estimates for selected points in the 2D space. 5. Analyze how LID patterns differ between datasets and correlate with sample quality/KL divergence. 6. Investigate relationships between LID estimates and local density/curvature estimates. 7. Compare LID evolution patterns between high-quality and low-quality samples to identify potential indicators of generation success.",
        "Interestingness": 9,
        "Feasibility": 10,
        "Novelty": 9,
        "novel": true
    },
    {
        "Name": "local_structure_preservation",
        "Title": "Analyzing and Enhancing Local Structure Preservation in Low-Dimensional Diffusion Models",
        "Experiment": "1. Implement a function to compute k-NN relationships for 2D data points. 2. Modify the sampling process to compute and store k-NN relationships at regular intervals during denoising (e.g., every 10 timesteps). 3. Implement a 'Local Structure Preservation Score' metric based on the consistency of k-NN relationships between original and denoised data. 4. Create 2D heatmap visualizations showing the evolution of local structure preservation during the diffusion process. 5. Modify the training loop to optionally include a local structure preservation term in the loss function. 6. Train models with both standard and structure-preserving approaches on all datasets. 7. Compare KL divergence, sample quality, and the new Local Structure Preservation Score between the two approaches across all datasets. 8. Analyze how local structure preservation patterns differ across datasets and correlate with final sample quality. 9. Investigate potential improvements in multi-modal generation and mode collapse prevention using the structure-preserving approach.",
        "Interestingness": 9,
        "Feasibility": 9,
        "Novelty": 9,
        "novel": true
    }
]