Conditioning Consistency Gap

• Conditioning consistency gap is the discrepancy between provided conditioning signals and the outputs produced by models, measured by metrics like KL divergence.
• It appears across domains such as conditional neural processes, diffusion-based generation, and sequential decision agents, indicating inconsistencies in adherence to conditioning.
• Research focuses on mitigating this gap through adaptive scaling, decoupled guidance, and stateful commitment to maintain coherence over multiple inference steps.

Searching arXiv for the cited papers and closely related work on conditioning consistency gap. Conditioning consistency gap denotes a discrepancy between conditioning information and the behavior, distributions, or decisions induced by a model. In recent work, the term is formalized exactly in conditional neural processes as a KL divergence between two predictive conditionals (Young, 21 Apr 2026). In adjacent literatures, the same phenomenon appears as a mismatch between intended structural constraints and generated images, between text prompts and reference identity, between fixed external conditions and agent trajectories, between semantic evidence and committed navigation actions, and between probabilistic uncertainty and local tangent dynamics in chaotic surrogates (Ji et al., 30 Jun 2026, Chen et al., 1 Jun 2026, Mehta, 12 Feb 2026, Wang et al., 11 May 2026, Herz et al., 29 May 2026). The unifying theme is that conditioning is not merely provided to a model; it must remain coherent across inference steps, modalities, objectives, and update rules.

1. Conceptual scope and recurring failure modes

Across domains, the conditioning consistency gap appears when a model receives a conditioning signal that is either not followed strongly enough, followed too rigidly, or applied inconsistently over time. In AC3S, the gap is the mismatch between 3D-aware visual and textual constraints and the actual behavior of a diffusion model, with two characteristic regimes: under-adherence, where the model weakly follows 3D structure and pose, and over-adherence, where ControlNet conditioning becomes “overly restrictive,” suppresses the generative prior, and degrades photorealism (Ji et al., 30 Jun 2026). In identity-preserving text-to-video generation, the same logic appears as a tension between “high-level prompt controllability” and “low-level identity fidelity”: semantic adapters weaken identity, whereas latent reference injection can cause appearance copy-paste that overrides text (Chen et al., 1 Jun 2026).

The same pattern recurs in multimodal systems. ACTOR defines a single “driving affect” that conditions dialogue, voice, face, and body, and reports that making a modality affect-inconsistent significantly decreases the perception of driving affects; the paper also identifies “emotion dilution” when a modality is not emotion conditioned and the multimodal response is perceived as more neutral (Chang et al., 2023). In diffusion image editing, SimEdit argues that coarse or weakly aligned textual conditioning destabilizes inversion and produces cross-branch attention inconsistency, so the conditioning signal is present but not realized coherently in the model’s dynamics and attention maps (Zhan et al., 12 Jun 2026).

Sequential decision-making exposes a temporal variant of the same issue. For ReAct-style LLM agents, fixed prompts, tools, temperature, and inputs still yield 2.0–4.2 distinct action sequences per 10 runs on average, and highly inconsistent tasks are substantially less accurate (Mehta, 12 Feb 2026). ConsistNav names an “action consistency gap” in zero-shot ObjectNav: semantic evidence is repeatedly reinterpreted at each step without persistent commitment across the episode, producing oscillation between exploration and pursuit, abandonment near success, or unverified stopping (Wang et al., 11 May 2026). A plausible synthesis is that conditioning consistency gaps are not restricted to static condition-to-output mappings; they also arise when a conditioning signal must be preserved across a trajectory.

2. Formal probabilistic definition in conditional neural processes

The most explicit formalization is given for conditional neural processes (CNPs). A CNP maps a context set

$C=\{(x_i,y_i)\}_{i=1}^n$

to a Gaussian predictive family

$$p_\theta(y\mid x;C)=\mathcal N\big(y;\mu_\theta(x,r_C),\sigma_\theta(x,r_C)^2I\big), \qquad r_C=\frac1n\sum_{i=1}^n h(x_i,y_i),$$

with mean aggregation and factorized target predictions (Young, 21 Apr 2026). Such models satisfy marginalization consistency because the target joint factorizes, but they violate conditioning consistency in the Kolmogorov sense: adding a new observation to the context updates the representation by re-encoding rather than by conditioning within a globally consistent joint distribution.

The conditioning consistency gap is defined as

$$\Delta(x_*,y_*,x_+;C) = D_{\mathrm{KL}}\!\Big( p_\theta(y_+\mid x_+;C^+) \,\Big\|\, p_\theta(y_+\mid x_+;C) \Big),$$

where $C^+=C\cup\{(x_*,y_*)\}$. The quantity measures how much the predictive distribution at $x_+$ changes when a point is added to the context. For Gaussian conditionals, the paper gives a closed-form expression in terms of the changes in predictive mean and variance. Under bounded encoders and Lipschitz decoders, the main theorem shows that the gap decays as $O(1/n^2)$ in the context size $n$, and matching lower bounds show that this rate is tight (Young, 21 Apr 2026).

This result gives a precise sense in which CNPs are approximately consistent. The representation shift from adding one point is $O(1/n)$; Lipschitz continuity turns that into $O(1/n)$ changes in predictive mean and variance; and the Gaussian KL is locally quadratic, yielding an $O(1/n^2)$ gap. The paper states that the inconsistency is negligible for moderate context sizes but can be significant in the few-shot regime. In this formulation, the conditioning consistency gap is neither metaphorical nor merely diagnostic: it is a quantitatively controlled divergence between two conditionals.

3. Generative modeling: structure, identity, and editing

In diffusion-based synthetic data generation, AC3S treats the gap as a trade-off between 3D structural adherence and generative realism. ControlNet injects visual features by

$$p_\theta(y\mid x;C)=\mathcal N\big(y;\mu_\theta(x,r_C),\sigma_\theta(x,r_C)^2I\big), \qquad r_C=\frac1n\sum_{i=1}^n h(x_i,y_i),$$0

and AC3S introduces an explicit conditioning scale

$$p_\theta(y\mid x;C)=\mathcal N\big(y;\mu_\theta(x,r_C),\sigma_\theta(x,r_C)^2I\big), \qquad r_C=\frac1n\sum_{i=1}^n h(x_i,y_i),$$1

Empirically, $$p_\theta(y\mid x;C)=\mathcal N\big(y;\mu_\theta(x,r_C),\sigma_\theta(x,r_C)^2I\big), \qquad r_C=\frac1n\sum_{i=1}^n h(x_i,y_i),$$2 “almost never aligns with the visual prompt,” whereas large $$p_\theta(y\mid x;C)=\mathcal N\big(y;\mu_\theta(x,r_C),\sigma_\theta(x,r_C)^2I\big), \qquad r_C=\frac1n\sum_{i=1}^n h(x_i,y_i),$$3 causes over-conditioning artifacts such as oversimplified textures, blurred backgrounds, incoherent scenes, and reduced diversity. Pose fidelity exhibits threshold behavior around a just noticeable difference threshold, while image quality degrades monotonically as $$p_\theta(y\mid x;C)=\mathcal N\big(y;\mu_\theta(x,r_C),\sigma_\theta(x,r_C)^2I\big), \qquad r_C=\frac1n\sum_{i=1}^n h(x_i,y_i),$$4 increases. AC3S therefore trains a 3-layer MLP modulator to predict a per-sample $$p_\theta(y\mid x;C)=\mathcal N\big(y;\mu_\theta(x,r_C),\sigma_\theta(x,r_C)^2I\big), \qquad r_C=\frac1n\sum_{i=1}^n h(x_i,y_i),$$5 from $$p_\theta(y\mid x;C)=\mathcal N\big(y;\mu_\theta(x,r_C),\sigma_\theta(x,r_C)^2I\big), \qquad r_C=\frac1n\sum_{i=1}^n h(x_i,y_i),$$6 and $$p_\theta(y\mid x;C)=\mathcal N\big(y;\mu_\theta(x,r_C),\sigma_\theta(x,r_C)^2I\big), \qquad r_C=\frac1n\sum_{i=1}^n h(x_i,y_i),$$7, and supervises it by pseudo-labels chosen as the smallest $$p_\theta(y\mid x;C)=\mathcal N\big(y;\mu_\theta(x,r_C),\sigma_\theta(x,r_C)^2I\big), \qquad r_C=\frac1n\sum_{i=1}^n h(x_i,y_i),$$8 whose generated image falls into the aligned cluster containing the $$p_\theta(y\mid x;C)=\mathcal N\big(y;\mu_\theta(x,r_C),\sigma_\theta(x,r_C)^2I\big), \qquad r_C=\frac1n\sum_{i=1}^n h(x_i,y_i),$$9 output. On 50 ImageNet classes, the full system improves overall FID from 87.19 for 3D-DST to 71.24, and also improves downstream classification and pose estimation, including large gains when training only on synthetic data (Ji et al., 30 Jun 2026).

In identity-preserving text-to-video generation, ST-DRC frames the gap as a conflict between text semantics and reference-image identity. The method concatenates a VAE-encoded reference latent as an extra temporal slice, then uses Temporal-Adjacent Spatial-Shifted RoPE with reference positions

$$\Delta(x_*,y_*,x_+;C) = D_{\mathrm{KL}}\!\Big( p_\theta(y_+\mid x_+;C^+) \,\Big\|\, p_\theta(y_+\mid x_+;C) \Big),$$0

so that reference tokens are temporally adjacent but spatially disjoint from video tokens. This is designed to permit identity-aware retrieval while suppressing spatially aligned copy-paste. The framework further applies appearance-invariant reference augmentation, ArcFace-based identity and temporal identity consistency losses, and a three-stream classifier-free guidance rule

$$\Delta(x_*,y_*,x_+;C) = D_{\mathrm{KL}}\!\Big( p_\theta(y_+\mid x_+;C^+) \,\Big\|\, p_\theta(y_+\mid x_+;C) \Big),$$1

which separates text adherence from reference fidelity at inference time. On the reported benchmark, ST-DRC reaches FaceSim-Arc 0.631, FaceSim-Cur 0.671, and CLIP-Score 33.04, outperforming the compared baselines and incrementally improving identity preservation, prompt alignment, and motion quality across ablations (Chen et al., 1 Jun 2026).

SimEdit analyzes an editing-specific version of the gap. In inversion-based editing, textual conditioning shapes the velocity field $$\Delta(x_*,y_*,x_+;C) = D_{\mathrm{KL}}\!\Big( p_\theta(y_+\mid x_+;C^+) \,\Big\|\, p_\theta(y_+\mid x_+;C) \Big),$$2 and therefore inversion stability. Under bounded Jacobian and curvature assumptions, the reconstruction error satisfies

$$\Delta(x_*,y_*,x_+;C) = D_{\mathrm{KL}}\!\Big( p_\theta(y_+\mid x_+;C^+) \,\Big\|\, p_\theta(y_+\mid x_+;C) \Big),$$3

so smaller effective Lipschitz constants improve inversion stability. The paper measures directional deviation of local velocity directions and an attention divergence metric $$\Delta(x_*,y_*,x_+;C) = D_{\mathrm{KL}}\!\Big( p_\theta(y_+\mid x_+;C^+) \,\Big\|\, p_\theta(y_+\mid x_+;C) \Big),$$4 between source and target cross-attention. Increasing prompt precision from coarse to detailed to comprehensive reduces empirical Lipschitz estimates, reduces directional deviation, improves reconstruction, and lowers cross-branch attention divergence. SimEdit combines conditioning refinement with token-wise cross-branch attention control, separating structure-preserving tokens from edit-driving tokens and amplifying the latter by a factor $$\Delta(x_*,y_*,x_+;C) = D_{\mathrm{KL}}\!\Big( p_\theta(y_+\mid x_+;C^+) \,\Big\|\, p_\theta(y_+\mid x_+;C) \Big),$$5 during attention manipulation. On PIE-Bench, it improves both inversion reconstruction and editing performance over previous attention-manipulation approaches (Zhan et al., 12 Jun 2026).

Consistency distillation gives a closely related but more algebraic version of the same idea. In consistency trajectory models, the student uses a preconditioned consistency function

$$\Delta(x_*,y_*,x_+;C) = D_{\mathrm{KL}}\!\Big( p_\theta(y_+\mid x_+;C^+) \,\Big\|\, p_\theta(y_+\mid x_+;C) \Big),$$6

and the paper defines the consistency gap as the norm difference between the teacher denoiser and the optimal student denoiser implied by the chosen preconditioning. Analytic-Precond derives a generalized teacher ODE, optimizes the preconditioning coefficients analytically to reduce this gap, and reports $$\Delta(x_*,y_*,x_+;C) = D_{\mathrm{KL}}\!\Big( p_\theta(y_+\mid x_+;C^+) \,\Big\|\, p_\theta(y_+\mid x_+;C) \Big),$$7 to $$\Delta(x_*,y_*,x_+;C) = D_{\mathrm{KL}}\!\Big( p_\theta(y_+\mid x_+;C^+) \,\Big\|\, p_\theta(y_+\mid x_+;C) \Big),$$8 training acceleration in multi-step generation (Zheng et al., 5 Feb 2025). This suggests that conditioning consistency gaps can arise not only from conditioning signals themselves, but also from the parameterization used to enforce consistency between teacher and student trajectories.

4. Sequential agents and navigation

For LLM-based agents, the gap is behavioral rather than purely distributional. The study on behavioral consistency runs a ReAct-style agent 10 times per question on 100 HotpotQA “hard” questions for each of three models, yielding 3,000 runs total. It defines AnswerConsistency, UniqueSeqs, StepVarianceRatio, and the first divergence point under identical question, tools, prompts, termination rules, and temperature. Average unique action sequences per 10 runs are 2.0 for Claude Sonnet 4.5, 2.4 for GPT-4o, and 4.2 for Llama 3.1 70B; the corresponding step variance ratios are 18.1%, 28.1%, and 55.0% (Mehta, 12 Feb 2026).

The crucial result is that variance predicts failure. Tasks with $$\Delta(x_*,y_*,x_+;C) = D_{\mathrm{KL}}\!\Big( p_\theta(y_+\mid x_+;C^+) \,\Big\|\, p_\theta(y_+\mid x_+;C) \Big),$$9 achieve 84.8%, 80.1%, and 92.0% accuracy for Claude Sonnet 4.5, GPT-4o, and Llama 3.1 70B respectively, whereas tasks with $C^+=C\cup\{(x_*,y_*)\}$0 achieve 43.3%, 25.0%, and 60.0%, giving gaps of 41.5, 55.1, and 32.0 percentage points. For Llama 3.1 70B, 69% of divergence occurs at step 2, the first search query, and lowering temperature from 0.7 to 0.0 reduces action-sequence diversity from 4.2 to 2.2 while increasing correctness from 77.4% to 82.8% (Mehta, 12 Feb 2026). Here, the conditioning consistency gap is the spread of internal trajectories under fixed external conditions.

ConsistNav turns this temporal inconsistency into an explicit control problem. It introduces a semantic executive built from a Finite-State Executive Controller with

$C^+=C\cup\{(x_*,y_*)\}$1

a Persistent Candidate Memory

$C^+=C\cup\{(x_*,y_*)\}$2

and Stability-Aware Action Control (Wang et al., 11 May 2026). Each candidate stores a position $C^+=C\cup\{(x_*,y_*)\}$3, accumulated positive confidence $C^+=C\cup\{(x_*,y_*)\}$4, negative evidence $C^+=C\cup\{(x_*,y_*)\}$5, positive and negative observation counts, a consistency score $C^+=C\cup\{(x_*,y_*)\}$6, ITM history, failure flags, and cooldown timestamps. Viable candidates must satisfy conditions including $C^+=C\cup\{(x_*,y_*)\}$7, $C^+=C\cup\{(x_*,y_*)\}$8, and $C^+=C\cup\{(x_*,y_*)\}$9. Approach-to-Verify transitions are gated by proximity, and stopping is permitted only after multi-cue verification with sufficient target hits, confidence, observation count, positive-over-negative evidence, and ITM support.

The executive is training-free and leaves the detector and low-level planner unchanged; it controls when semantic evidence should influence navigation and when it should be suppressed or revisited. On HM3Dv2, HM3Dv1, and MP3D, ConsistNav reports SR/SPL of 84.2/41.2, 63.2/34.8, and 50.6/25.7. On MP3D it improves SR by 11.4% and SPL by 7.9% over the controlled baseline, and ablations show monotonic gains from Persistent Candidate Memory, then Finite-State Executive Control, then Stability-Aware Action Control (Wang et al., 11 May 2026). In this setting, the conditioning consistency gap is closed by converting per-step semantic re-interpretation into persistent, stateful commitment.

5. Dynamical systems and decision-theoretic foundations

Chaotic surrogate modeling exposes a dynamic-probabilistic variant of the gap. The DPC gap is defined by a refinement $x_+$0 such that a finite-horizon probabilistic objective $x_+$1 improves,

$x_+$2

while a certification loss $x_+$3 degrades,

$x_+$4

The paper identifies three mechanisms: core collapse, in which open-loop Gaussian rollout likelihood penalizes Jacobian-generated covariance growth and encourages weaker physical expansion; noise masking, in which flexible shell noise absorbs errors without repairing the core dynamics; and blind uncertainty, in which predictive variance is decoupled from local tangent expansion (Herz et al., 29 May 2026).

KAFFEE addresses this by training through a differentiable extended Kalman filter. Its latent covariance recursion is

$x_+$5

and the loss is the innovation likelihood rather than an open-loop rollout likelihood. On stochastic hyperchaotic Lorenz–96, KAFFEE improves reconstruction of dynamical invariants relative to open-loop objectives, achieves the highest tangent-alignment score $x_+$6, and maintains competitive predictive scores. The same paper shows that the DPC gap also appears when probabilistically adapting a DSR foundation model across 13 chaotic systems, and that KAFFEE largely preserves zero-shot dynamics while enabling in-context Bayesian filtering (Herz et al., 29 May 2026). This extends conditioning consistency from static conditional distributions to a setting in which uncertainty should be transported by the same Jacobians that define the learned dynamics.

A more abstract antecedent appears in the theory of conditional nonlinear expectations. For a family

$x_+$7

of conditional nonlinear expectations, time consistency is

$x_+$8

Under strict monotonicity and pointwise continuity of $x_+$9, the paper proves that such a time-consistent family exists if and only if it has a conditional certainty-equivalent representation induced by a state-dependent utility $O(1/n^2)$0: $O(1/n^2)$1 At the preference level, the paper shows that the Sure-Thing Principle is equivalent to conditionability on every sub-$O(1/n^2)$2-algebra and thus to the existence of consistent backward conditional projections (Berton et al., 2024). In this decision-theoretic setting, the conditioning consistency gap appears axiomatically: once consistency across all $O(1/n^2)$3-algebras is required, admissible nonlinear evaluations collapse to conditional certainty equivalents.

6. Diagnostics, empirical signatures, and research directions

The literature converges on several recurring diagnostics. In CNPs, the gap is a KL divergence between two predictive conditionals and admits asymptotic bounds in context size (Young, 21 Apr 2026). In diffusion systems, it appears as threshold behavior in pose adherence, monotonic degradation in realism, inversion reconstruction error, attention divergence, or the gap between teacher and student denoisers under a chosen preconditioning (Ji et al., 30 Jun 2026, Zhan et al., 12 Jun 2026, Zheng et al., 5 Feb 2025). In text-to-video and multimodal affect generation, it is measured through identity metrics, CLIP alignment, motion quality, or human perception of the intended driving affect under consistent and inconsistent modality conditioning (Chen et al., 1 Jun 2026, Chang et al., 2023). In agents and navigation, it is observable as path diversity, first divergence points, unstable commitment, timeout rates, or oscillation between semantic modes (Mehta, 12 Feb 2026, Wang et al., 11 May 2026). In chaotic surrogates, it requires joint dynamical and probabilistic diagnostics, including Lyapunov-spectrum errors, state-space divergence, and tangent-alignment metrics such as $O(1/n^2)$4 (Herz et al., 29 May 2026).

A common empirical lesson is that fixed global conditioning rules are often inadequate. AC3S reports that the optimal conditioning scale “cannot generalize across class categories and even varies with different random seeds for the same $O(1/n^2)$5” (Ji et al., 30 Jun 2026). ST-DRC separates text and reference guidance at inference time rather than relying on a single merged control stream (Chen et al., 1 Jun 2026). SimEdit improves consistency by refining conditioning signals before editing and then treating structure-preserving and edit-driving tokens asymmetrically (Zhan et al., 12 Jun 2026). ReAct-agent experiments show that runtime monitoring of trajectory agreement could support early error detection, and ConsistNav shows that a semantic executive can impose persistent commitment without retraining the detector or planner (Mehta, 12 Feb 2026, Wang et al., 11 May 2026). KAFFEE similarly replaces open-loop rollout scoring with innovation-based filtering to keep uncertainty aligned with local Jacobian transport (Herz et al., 29 May 2026).

Taken together, these results suggest a general research program. One direction is consistency-aware control of conditioning strength, whether via adaptive $O(1/n^2)$6 modulation, decoupled guidance, or analytically optimized preconditioning (Ji et al., 30 Jun 2026, Chen et al., 1 Jun 2026, Zheng et al., 5 Feb 2025). A second is cross-channel and cross-time coherence, enforced by structured prompts, memory, state machines, or filtering recursions (Zhan et al., 12 Jun 2026, Wang et al., 11 May 2026, Herz et al., 29 May 2026). A third is evaluation beyond endpoint performance: a model may optimize NLL, FID, or pass@1 while still exhibiting a substantial conditioning consistency gap in its internal trajectories, uncertainty transport, or cross-modal agreement. In that sense, conditioning consistency gap has become a cross-disciplinary label for a precise family of failures: the external condition is available, but the induced computation does not remain faithful to it.