Composable Guidance Methods

• Composable Guidance (CoG) is a methodological pattern that composes condition-specific signals—via weighted scores, energy functions, or logical calculus—to steer outputs in various tasks.
• It leverages additive and modular techniques to enable fine-grained control across applications like molecular design, image generation, and robot navigation.
• By fusing reusable strategies and mathematical operators, CoG significantly improves controllability and transparency while reducing the need for retraining for every condition combination.

Searching arXiv for papers on composable guidance and related formulations. Composable Guidance (CoG) denotes a family of methods in which multiple guidance signals are combined to steer generation, planning, or reasoning without training a separate model for every condition combination. In the literature represented here, the composition may take the form of weighted score sums, additive energy functions, recursive logical scores, value propagation across mixed datasets, or portfolios of reusable strategies. The acronym is also polysemous: some papers use CoG to denote compositional guidance itself, while others attach the label to distinct frameworks such as "COG: Connecting New Skills to Past Experience with Offline Reinforcement Learning" (Singh et al., 2020) and "CoG: Controllable Graph Reasoning via Relational Blueprints and Failure-Aware Refinement over Knowledge Graphs" (Liu et al., 16 Jan 2026).

1. Terminology and scope

In its narrowest use, CoG refers to inference-time composition of condition-specific guidance terms. This is explicit in the Composable Score-based Graph Diffusion model, which introduces Composable Guidance (CoG) for flexible multi-conditional molecular generation and emphasizes selective emphasis on arbitrary subsets of properties during sampling (Qiao et al., 11 Sep 2025). Closely related uses appear in CoCo-Bot, which is described as strongly aligned with the spirit of CoG because it steers a generator through composable concept energies rather than hidden auxiliary channels, and in ComposableNav, which learns separate diffusion primitives and composes their denoising outputs at deployment time (Kim et al., 11 Jul 2025, Hu et al., 22 Sep 2025).

The same label is also attached to broader architectures in which composability is not limited to diffusion guidance. In visual analytics, Lotse treats guidance as a portfolio of reusable strategies and actions; in KG reasoning, CoG combines relational blueprint guidance with failure-aware refinement; in multimodal reasoning, COGS recomposes perception and reasoning factors into new supervision; and in large-model adaptation, structural priors guide modular adapter composition (Sperrle et al., 2022, Liu et al., 16 Jan 2026, Gu et al., 16 Oct 2025, Wang et al., 6 Nov 2025). This suggests that "Composable Guidance" is best understood as a methodological pattern rather than a single canonical algorithm.

Work	Domain	Composition object
CoCo-Bot (Kim et al., 11 Jul 2025)	Interpretable image generation	Weighted concept energies
ComposableNav (Hu et al., 22 Sep 2025)	Dynamic robot navigation	Primitive denoiser outputs
CSGD/CoG (Qiao et al., 11 Sep 2025)	Molecular graph diffusion	Property-specific score offsets
LoGDiff (Alesiani et al., 5 Feb 2026)	Logical conditional generation	Posterior-weighted Boolean scores
OmniGuide (Song et al., 9 Mar 2026)	Generalist robot policies	Additive 3D energy fields

2. Core mathematical patterns

A recurring mathematical motif is the decomposition of a joint condition into reusable condition-specific terms around a base prior. In ComposableNav, the conditional trajectory distribution is factorized as

$$p(\tau \mid \phi^{(1)}, o^{(1)}, \cdots, \phi^{(k)}, o^{(k)}) \propto p(\tau)\prod_{i=1}^{k}\frac{p(\tau\mid \phi^{(i)}, o^{(i)})}{p(\tau)},$$

and the composed sampler sums the predicted noises from the primitive denoisers at test time (Hu et al., 22 Sep 2025). In CSGD, CoG takes the classifier-free style form

$$s_\theta^{\mathrm{CoG}}(G_t,\mathcal{C},t) = s_\theta(G_t,\varnothing,t) + \sum_{m=1}^{M} w_m \Bigl(s_\theta(G_t,c_m,t) - s_\theta(G_t,\varnothing,t)\Bigr),$$

so guidance is the unconditional score plus weighted property-specific offsets (Qiao et al., 11 Sep 2025).

Energy-based variants instantiate the same pattern with additive potentials rather than additive scores. CoCo-Bot defines concept-conditioned generation through a total energy

$$\mathcal{E}_\theta(v_t; \mathbf{C}, t) = \sum_{k=1}^K e_\theta(v_t, c_k, t),$$

and interventions use a weighted energy sum

$$\mathcal{E}_\theta^{\mathrm{interv}}(v_t; \mathbf{C}, \mathbf{w}, t) = \sum_{k=1}^K w_k\, e_\theta(v_t, c_k, t),$$

with $w^+=1$ for activating a concept and $w^-=-0.001$ for negating it (Kim et al., 11 Jul 2025). OmniGuide likewise augments a base flow-matching vector field with a guidance gradient,

$$\mathbf{v}_\theta(\mathbf{A}^{\tau}, \mathbf{o}\mid \mathbf{y}) = \mathbf{v}_\theta(\mathbf{A}^{\tau}, \mathbf{o}) + \lambda_\tau \nabla_{\mathbf{A}^{\tau}} \log p(\mathbf{y}\mid \mathbf{A}^{\tau}),$$

and composes heterogeneous robot guidance sources by summing their energies and gradients (Song et al., 9 Mar 2026).

Logical variants replace fixed weights with state-dependent coefficients derived from posterior probabilities. LoGDiff defines the logical score

$$s_t(\varphi, x) := \nabla_x \log p_t(\varphi \mid x),$$

and shows that conjunction, negation, and two forms of disjunction can be composed exactly when the Boolean formula admits a circuit representation with appropriate conditional-independence or mutual-exclusivity structure (Alesiani et al., 5 Feb 2026). A plausible implication is that CoG spans at least three mathematically distinct operators—offset addition, energy superposition, and recursive logical calculus—even when the high-level purpose is the same.

3. Diffusion and generative modeling

In generative modeling, CoG is primarily used to improve controllability without retraining the backbone generator for every composition. CoCo-Bot is a post-hoc concept bottleneck generative model that removes auxiliary visual cues at the bottleneck and routes generation only through explicit human-interpretable concepts. Using StyleGAN2 pre-trained on CelebA-HQ, it reports concept accuracy of 75.70% versus 74.38% for CC-AE and FID of 9.74 versus 9.77, while supporting interventions such as single-concept edits, multi-concept composition, and negation including examples like Smile + Attractive + ¬Male and Male → ¬Male (Kim et al., 11 Jul 2025). The central claim is that transparent compositional control improves because some generation-relevant information no longer flows through non-concept channels.

CSGD extends score matching to discrete molecular graphs via concrete scores and uses CoG for multi-property molecular design. The stated motivation is that joint conditioning obscures the influence of individual properties and hinders fine-grained control, while predictor-guidance-style methods often require continuous relaxations that can hurt discrete graph fidelity. Across four molecular datasets, the paper reports a 15.3% average improvement in controllability over prior methods while maintaining high validity and distributional fidelity, and it directly evaluates subset conditioning such as only Synthesizability, only Gas Permeability properties, or mixed subsets like $\{\text{Synth.}, \text{O}_2\}$ (Qiao et al., 11 Sep 2025). Probability Calibration is introduced as an optional post-processing step to mitigate train-test mismatch in guided transition probabilities.

LoGDiff studies a more stringent question: when can composition be exact rather than heuristic? It derives an exact Boolean calculus for logical guidance in diffusion models. Under the paper’s sufficient conditions, conjunctions combine conditionally independent subformulas, and disjunctions combine subformulas that are either conditionally independent or mutually exclusive. The recursive rules then reproduce the exact posterior and exact logical score from atomic scores and posterior probabilities (Alesiani et al., 5 Feb 2026). Empirically, the paper reports that LoGDiff strongly outperforms constant-weight baselines on disjunctions and complex nested formulas, including OR-ME: 98.0% vs 77.0% on CMNIST and OR-ME: 94.3% vs 63.3% on Shapes3D, while also demonstrating image and protein structure generation.

Visual-CoG broadens the generative interpretation by treating guidance as a staged reinforcement signal rather than a single compositional score. Its Visual-Chain of Guidance consists of semantic reasoning, process refining, and outcome evaluation, with total reward

$$\mathcal{R}= \mathcal{R}_{r} + \mathcal{R}_{p} + \mathcal{R}_{o}.$$

On GenEval, T2I-CompBench, and VisCog-Bench, it reports improvements of 15%, 5%, and 19%, respectively, and attributes the gains to stage-aware rewards that provide better credit assignment than final-only supervision (Li et al., 25 Aug 2025). This is not CoG in the strict score-composition sense, but it preserves the broader principle that complex generation should be guided through decomposable intermediate signals.

4. Robotics and embodied control

In robotics, composable guidance is used to satisfy simultaneous behavioral constraints in environments where enumerating all task combinations is impractical. ComposableNav formulates each instruction as a set of constituent specifications and learns one diffusion model per motion primitive, such as pass from the left, pass from the right, follow behind a person, yield to a person, walk through a region, and avoid walking through a region. It uses a two-stage pipeline: supervised pre-training of a base diffusion planner on general dynamic-navigation data, followed by DDPO-based RL fine-tuning for each primitive (Hu et al., 22 Sep 2025). In simulation, six motion primitives are combined into 24 instructions spanning combinations of 2, 3, and 4 specifications, with 20 random environments per instruction. Reported overall success rates are 99.8%, 75.5%, 58.6%, and 34.9% for 1-, 2-, 3-, and 4-primitive settings, substantially exceeding VLM-Social-Nav, CoNVOI, and BehAV. In real-world tests, initial planning with four composed primitives takes about 0.413 s and replanning about 0.060 s.

OmniGuide provides a different robotics instantiation: inference-time guidance for pretrained vision-language-action policies through differentiable 3D energy fields. The framework converts external signals from 3D foundation models, semantic-reasoning VLMs, and human pose models into attractive or repulsive fields over predicted Cartesian trajectories, then backpropagates the corresponding gradients into the action-sampling process (Song et al., 9 Mar 2026). The abstract reports an overall increase from 24.2% to 92.4% success and from 7.0% to 93.5% collision-free safety. In simulation, initialization guidance improves success by 8% and reduces collisions by 18%, denoising guidance improves success by 20% and reduces collisions by 34%, and combining both improves success by 26% and reduces collisions by 46%. The framework is explicitly compositional because multiple guidance sources are fused as additive energies rather than through bespoke controllers.

A third robotics lineage uses composability without diffusion. "COG: Connecting New Skills to Past Experience with Offline Reinforcement Learning" applies conservative Q-learning to the union of sparse-reward task data and unlabeled prior data, allowing Bellman backups to stitch together behaviors across datasets (Singh et al., 2020). The hardest experimental setting composes four robotic skills in a row—picking, placing, drawer opening, and grasping—using only a $$s_\theta^{\mathrm{CoG}}(G_t,\mathcal{C},t) = s_\theta(G_t,\varnothing,t) + \sum_{m=1}^{M} w_m \Bigl(s_\theta(G_t,c_m,t) - s_\theta(G_t,\varnothing,t)\Bigr),$$0 sparse reward on task completion. On the drawer grasping task, reported success rates are 0.98 for open drawer, 0.68 for closed drawer, 0.78 for blocked drawer 1, and 0.76 for blocked drawer 2; on the real WidowX drawer task, COG succeeds in 7/8 trials when the drawer starts closed. Here the compositional mechanism is value propagation through prior experience rather than explicit score or energy composition.

5. Reasoning, analytics, and modular learning systems

Composable guidance also appears in reasoning systems that combine structural priors with corrective procedures. In KG reasoning, CoG is a training-free framework inspired by Dual-Process Theory. Its Relational Blueprint Guidance module provides soft structural constraints through relation-only templates extracted from training paths, while Failure-Aware Refinement triggers evidence-conditioned reflection and controlled backtracking when reasoning stagnates (Liu et al., 16 Jan 2026). The framework is evaluated on WebQSP, CWQ, and GrailQA with GPT-3.5, GPT-4, and Qwen2.5-7B; reported GPT-4 results are 77.8 on CWQ, 89.7 on WebQSP, and 86.4 overall on GrailQA. In this setting, composability lies in the coordinated use of a fast structural prior and a slower corrective controller.

In visual analytics, Lotse operationalizes guidance as software architecture. It introduces strategy templates with fields such as guidance goal, guidance level, guidance degree, timing, adaptation, placement, and visual elements, and implements them in a Python library that exposes a REST API and websockets for asynchronous suggestion delivery (Sperrle et al., 2022). Strategies have callbacks such as determine_applicability, is_applicable, generate_suggestion_content, should_retract, accept, and reject, while a meta-strategy arbitrates among multiple active suggestions. The paper characterizes this as a practical route toward reusable guidance strategies and a first step toward a grammar of guidance.

In large-model adaptation, structural priors and modular adapters produce a guidance-like mechanism over reusable submodules. The method models dependencies with a relation matrix, propagates them with a graph-convolution-style update,

$$s_\theta^{\mathrm{CoG}}(G_t,\mathcal{C},t) = s_\theta(G_t,\varnothing,t) + \sum_{m=1}^{M} w_m \Bigl(s_\theta(G_t,c_m,t) - s_\theta(G_t,\varnothing,t)\Bigr),$$1

and aggregates adapter outputs as

$$s_\theta^{\mathrm{CoG}}(G_t,\mathcal{C},t) = s_\theta(G_t,\varnothing,t) + \sum_{m=1}^{M} w_m \Bigl(s_\theta(G_t,c_m,t) - s_\theta(G_t,\varnothing,t)\Bigr),$$2

with coefficients guided by the structural prior (Wang et al., 6 Nov 2025). On OGBG-MolPCBA, the reported comparison is G-Adapter: 5.20M params, AP 22.6, AWA 78.5; GPS++: 8.50M params, AP 23.1, AWA 80.0; GraphAdapter: 6.70M params, AP 22.9, AWA 79.2; Ours: 4.80M params, AP 23.7, AWA 83.1. The paper explicitly frames this as conceptually aligned with CoG even though the guidance signal is a graph structural prior rather than a diffusion score.

COGS applies a related principle to multimodal reasoning data generation. Seed questions are decomposed into primitive perception and reasoning factors, recomposed with new images, and paired with subquestions and intermediate answers for GRPO-based RL fine-tuning (Gu et al., 16 Oct 2025). On ChartQAPro, the reported performance is 47.36 for Qwen2.5-VL-7B base and 52.02 for COGS; on VisualWebBench, 85.65 rises to 88.04. The reward ablation reports StandardRM: 50.96, ProcessRM-sum: 50.35, and ProcessRM-max: 52.02, with the paper arguing that ProcessRM-max preserves policy order under a noisy shaping-reward assumption. This broadens the meaning of composable guidance from inference-time signal fusion to the synthesis of reusable reasoning factors and process-level rewards.

6. Assumptions, limitations, and open questions

The strongest theoretical forms of CoG are conditional. In CSGD, the central decomposition assumes conditional independence of properties given the graph,

$$s_\theta^{\mathrm{CoG}}(G_t,\mathcal{C},t) = s_\theta(G_t,\varnothing,t) + \sum_{m=1}^{M} w_m \Bigl(s_\theta(G_t,c_m,t) - s_\theta(G_t,\varnothing,t)\Bigr),$$3

and the paper explicitly notes that handling correlated conditions remains an important direction for future research (Qiao et al., 11 Sep 2025). In LoGDiff, exactness requires a circuit representation whose conjunctions and disjunctions satisfy the stated conditional-independence or mutual-exclusivity constraints, and the method also depends on accurate posterior estimation; the paper notes that errors can be amplified, especially in negation due to the factor $$s_\theta^{\mathrm{CoG}}(G_t,\mathcal{C},t) = s_\theta(G_t,\varnothing,t) + \sum_{m=1}^{M} w_m \Bigl(s_\theta(G_t,c_m,t) - s_\theta(G_t,\varnothing,t)\Bigr),$$4 (Alesiani et al., 5 Feb 2026). In ComposableNav, the authors acknowledge that the direct sum of primitive denoisers with uniform weights $$s_\theta^{\mathrm{CoG}}(G_t,\mathcal{C},t) = s_\theta(G_t,\varnothing,t) + \sum_{m=1}^{M} w_m \Bigl(s_\theta(G_t,c_m,t) - s_\theta(G_t,\varnothing,t)\Bigr),$$5 can degrade as the number of specifications grows and that the approach is not a full solution to compositional reasoning (Hu et al., 22 Sep 2025).

A second recurring limitation concerns guidance strength and prior conflict. OmniGuide reports that increasing $$s_\theta^{\mathrm{CoG}}(G_t,\mathcal{C},t) = s_\theta(G_t,\varnothing,t) + \sum_{m=1}^{M} w_m \Bigl(s_\theta(G_t,c_m,t) - s_\theta(G_t,\varnothing,t)\Bigr),$$6 improves safety, but overly large values begin to conflict with the pretrained policy’s naturalness prior and can reduce success; it also notes dependence on the quality of reconstruction, VLM localization, and human pose estimation, along with a roughly $$s_\theta^{\mathrm{CoG}}(G_t,\mathcal{C},t) = s_\theta(G_t,\varnothing,t) + \sum_{m=1}^{M} w_m \Bigl(s_\theta(G_t,c_m,t) - s_\theta(G_t,\varnothing,t)\Bigr),$$7 slowdown relative to the base VLA (Song et al., 9 Mar 2026). CSGD introduces Probability Calibration because large guidance scales can improve property adherence but harm fidelity and validity through train-test mismatch (Qiao et al., 11 Sep 2025). In visual analytics, Lotse is intentionally hybrid rather than fully declarative, depends on the design of the analysis state vector, and is presented as a first step rather than a complete grammar (Sperrle et al., 2022).

A common misconception is that any mechanism called CoG necessarily performs exact or universal composition. The surveyed literature does not support that interpretation. Some systems offer exact logical composition under explicit structural assumptions; some provide heuristic or approximate composition through score or energy summation; some rely on modular software orchestration; and some obtain compositional behavior implicitly through value propagation or process supervision (Alesiani et al., 5 Feb 2026, Singh et al., 2020, Gu et al., 16 Oct 2025). A plausible implication is that future progress will depend less on the label itself than on three concrete issues already identified in these papers: better handling of correlated or non-independent conditions, more reliable posterior or perception estimates for guidance coefficients, and richer control operators that remain faithful as the number of composed constraints increases.