Custom Diffusion Models for Generative Tasks

• Custom Diffusion Models (CDMs) are generative models that extend traditional diffusion processes through tailored architectures, training protocols, and inference strategies.
• They incorporate advanced techniques such as algebraic extensions, flexible SDE parameterization, and cascaded pipelines to enhance sample quality and robustness.
• Modular designs in CDMs support continual learning, selective forgetting, and few-shot personalization, improving performance on tasks like molecular generation and image synthesis.

Custom Diffusion Models (CDMs) refer to a broad family of diffusion-based generative models with mechanisms tailored for domain, data, or task specificity. The term encompasses models customized via: (1) structure—alterations to architecture, embedding space, or algebraic setting; (2) training—modifications for robustness, continual learning, or modular use; and (3) inference—composition, selective forgetting, or context-aware synthesis. Core properties include flexibility in noise processes, parameterization, conditioning, and model adaptation across high-dimensional and structured data types, enabling competitive performance and addressing practical requirements in generative learning.

1. Algebraic and Representational Extensions

A fundamental direction in CDMs is extending the standard real-vector feature space to richer algebraic structures, as exemplified by Clifford Diffusion Models (CDMs) for 3D molecular generation (Liu et al., 22 Apr 2025). Here, data samples—such as molecular coordinates—are embedded in the graded Clifford algebra $\text{Cl}(\mathbb{R}^3)$, a space of multivectors with scalar (grade-0), vector (grade-1), bivector (grade-2), and trivector (grade-3) components. Raw input data are mapped to specific grades, with higher grades encoding learned geometric or relational features. This embedding enables the model to capture the joint distribution over all subspaces of the algebra, incorporating geometric invariance through Clifford group actions. Forward and reverse diffusion steps are performed independently per grade, leveraging a Clifford-equivariant neural network (e.g., Clifford-EGNN) that computes message passing via geometric products rather than standard linear algebra. Empirical results demonstrate competitive validity, stability, and diversity in small molecule generation, with the most expressive (all-grade) variant attaining highest uniqueness and validity among diffusion-based generative baselines (Liu et al., 22 Apr 2025).

2. Flexible Forward and Reverse Diffusion Process Parameterization

CDMs offer flexibility in specifying the diffusion (noising) process, allowing domain-adaptive and theoretically principled SDEs. The FP-Diffusion framework (Du et al., 2022) generalizes the forward SDE to

$dx_t = f_t(x_t) dt + g_t(x_t) dW_t$

with spatially-parameterized metric $R(x)$ (learned positive-definite matrix) and antisymmetric mixing $\omega$, both learnable via small neural networks. This enables the design of custom forward drifts and diffusions, including standard VP-SDE (Ornstein-Uhlenbeck), sub-VP SDE, and critically-damped Langevin diffusions. Provided mild assumptions, the framework guarantees well-posedness and ergodic stationary laws. The resulting family expands the variational bound expressivity and allows empirical optimization for data-specific structure, as demonstrated by reduced NLL and improved sample quality on MNIST and CIFAR-10 (Du et al., 2022).

3. Modular, Compositional, and Privacy-Aware Architectures

Compartmentalized/Compositional Diffusion Models (Golatkar et al., 2023) decompose a generative model into $n$ independently trained modules or “adapters,” each on a distinct data shard. At inference, the overall score function is computed as a mixture of the constituent module scores, weighted via an estimated mixture classifier. This supports several capabilities:

• Perfect Selective Forgetting: Immediate removal of any data subset by deleting its corresponding module.
• Continual Learning: New data are incorporated by training only new modules, avoiding catastrophic forgetting.
• Access-Based Customization: Users restricted to specific data shards are served by dynamically composing only permitted modules.
• Efficient Unlearning: Forgetting requires retraining only the affected module rather than the monolithic model (up to $n$x reduction in cost).

Empirically, CDMs with 8 splits on CUB-200 data maintain FID within 10% of monolithic models and improve text-to-image alignment (TIFA) over joint training. This architecture enables granular data protection, scalable continual learning, and attribution analysis, at the expense of increased storage and inference cost, which can be mitigated by lightweight adapters (Golatkar et al., 2023).

4. Conditional, Robust, and Few-shot Customization

Several CDMs are designed for conditional data generation and robust adaptation:

• RCDM (Robust Conditional Diffusion Model): Mitigates fixed-error accumulation in conditional reverse processes by dynamically adjusting classifier-free guidance weights using a control-theoretic approach. It deploys two denoising networks and computes an optimal guidance parameter $w^*$ as an analytic function of error, preventing mode collapse under input perturbation with negligible computational overhead. Experimental evidence covers robustness restoration on MNIST and CIFAR-10 under strong synthetic biases (Xu et al., 2024).
• Few-Shot Conditional Distribution Modeling: For few-shot synthesis, the CDM framework leverages a latent diffusion model conditioned on feature vectors whose full (Gaussian) distribution is calibrated from nearest seen-class statistics and optimized via inversion. This resolves the diversity-fidelity tradeoff endemic to few-shot settings by borrowing strength from data-rich classes and refining to the support set (Gupta et al., 2024).

CDMs have also been customized for continuous label conditioning (regression settings) via the Continuous Conditional Diffusion Model (CCDM) (Ding et al., 2024), using MLP-based label embeddings and hard vicinal image-denoising objectives for improved label-consistency, as well as for text-to-image continual personalization under the Concept-Incremental Diffusion Model (CIDM) (Dong et al., 2024), which combines orthogonal and shared-subspace regularization, elastic module aggregation, and context-controllable synthesis for robust, multi-concept lifelong learning.

5. Cascaded and Structured Pipelines

Custom Diffusion Models include cascaded architectures that decompose high-dimensional output synthesis into a pipeline of base and super-resolution diffusion models (Ho et al., 2021, Habibi et al., 2024). Each stage generates at increasing resolution, with later models conditioned on upsampled (possibly noised/augmented) output from previous ones. Conditioning augmentation via noise (for low resolution) and Gaussian blur (for high resolution) is critical to prevent compounding artifacts and enable SR models to handle distributional shift in their inputs. Empirical results on ImageNet show that such CDMs outperform competitors (e.g., BigGAN, VQ-VAE-2, SR3) in both FID and classification accuracy scores at high resolutions (Ho et al., 2021). Conditional cascaded diffusion models (cCDM) have also been applied for multi-resolution inverse design in engineering applications, supporting the independent tuning of pipeline stages and robust constraint satisfaction when data are sufficient (Habibi et al., 2024).

6. Output Likelihood, Density Ratio, and Feature Distillation

Some CDMs are constructed to provide tractable likelihood estimation—historically missing in most diffusion models—by tightly linking denoising and density-ratio estimation (DRE) via classification. Classification Diffusion Models (Yadin et al., 2024) train a network to classify noise levels and use the gradient of classifier logits as the minimum-MSE denoiser. This design admits exact likelihood computation at any diffusion step and substantially improves single-pass negative log-likelihood (NLL), matching or exceeding modern flow-based models (e.g., NLL ≈ 3.38 on CIFAR-10, or 2.98 for a uniform-schedule variant) with no loss in sample quality.

In addition to synthesis, CDMs serve as compact, interpretable teachers for discriminative models. Canonical Latent Representations (CLAReps) are derived by projecting out latent directions that encode spurious, non-class-defining variance, providing class-prototypical latents whose decodings summarize each class with minimal context. Student networks trained via feature distillation from CLAReps (CaDistill) inherit adversarial robustness and strong generalization, with only 10% of data required for teacher transfer (Xu et al., 11 Jun 2025).

7. Customization for User-Guided and Lifelong Personalization

CDMs provide efficient user-level customization in large, pretrained text-to-image models:

• Custom-Edit: Adapts only “language-relevant” parameters (rare token embedding and selected cross-attention projections) to teach a diffusion model new concepts from a handful of reference images. This process is modular—decoupling customization from editing (e.g., via Prompt-to-Prompt or SDEdit inversion)—and data efficient (optimization over ≈50 MB of parameters, 500 steps). The resulting customized model achieves superior reference similarity/source similarity trade-offs versus full fine-tuning or textual inversion (Choi et al., 2023).
• CIDM: Formalizes concept-incremental customization as the continual learning of LoRA-adapted modules, regulated by concept consolidation loss and elastic aggregation, with context-aware inference via spatial cross-attention and region-wise noise fusion. This design solves both catastrophic forgetting of personalized concepts and “concept neglect" in region-conditioned multi-concept image synthesis (Dong et al., 2024).

Table: Representative Custom Diffusion Models and Customization Modalities

Model/Approach	Customization Axis	Key Capability
Clifford Diffusion Model	Algebraic/model structure	$\mathrm{E}(3)$-equivariance for molecular gen. (Liu et al., 22 Apr 2025)
Compositional Diffusion	Modular training/inference	Continual learning, selective forgetting (Golatkar et al., 2023)
RCDM	Error-robust inference	Robust denoising under bias (Xu et al., 2024)
cCDM / Cascaded	Pipeline/decomposition	Multi-resolution synthesis (Ho et al., 2021, Habibi et al., 2024)
CCDM	Conditioning/objective	Continuous label conditioning (Ding et al., 2024)
CaDistill	Representation-layer	Compact, robust feature distillation (Xu et al., 11 Jun 2025)
Custom-Edit, CIDM	Personalization/lifelong	Few-shot user concept learning, region control (Choi et al., 2023, Dong et al., 2024)

CDMs therefore represent a design space in which the diffusion modeling paradigm is extended, modularized, and adapted to match both the structure of specific data and the needs of end-users, providing new levels of control, interpretability, privacy, and efficiency across generative tasks.