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Chameleon: Dynamic Format Adapter for Efficient Diffusion
Arnab Sanyal, Sandeep Chinchali
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Abstract
Abstract:Post-training quantization (PTQ) is the standard way to run modern diffusion models on memory-constrained accelerators, yet every existing diffusion PTQ scheme fixes the $\mathit{number\ format}$ in advance and only tunes the scale, zero point, or per-layer bit-width. At a fixed bit-width the best format depends on the distribution being encoded, and that distribution differs across weight channels, across layers, and along the diffusion timestep, where activation distributions slide from heavy-tailed and noise-dominated to tightly clustered and structured. We propose Chameleon, a PTQ framework that holds the bit-width fixed and treats the format itself as a discrete variable, chosen per weight channel and per (layer, timestep bucket) activation tensor. Activation formats come from {INT8, FP8 E4M3, FP8 E5M2, MXFP8, MXINT8}, selected ahead of time from two cheap statistics (empirical kurtosis and the closed-form diffusion SNR) and stored in a lookup table; weight formats come from {INT8, MXINT8} at 8 bits or {INT4, NF4, FP4 E2M1, MXINT4, MXFP4} at 4 bits, selected offline by reconstruction error. An architectural fork adapts the same selection layer to multi-step UNets, single-step distilled models, and Diffusion Transformers. Across SDXL, SDXL-Turbo, and PixArt-$\alpha$ on COCO-2014, Chameleon achieves the best FID in all six backbone $\times$ bit-width settings, with CLIP within 0.24 of the FP16 reference and the best of all quantized methods at $W_{4}A_{8}$.
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- Source: https://arxiv.org/abs/2609.33496v1
- Canonical: https://arxiv.org/abs/2609.33496v1
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CHAMELEON: DYNAMIC FORMAT ADAPTER FOR EFFICIENT DIFFUSION Arnab Sanyal & Sandeep Chinchali UT SWARM Lab, Department of Electrical & Computer Engineering The University of Texas, Austin TX 78712 sanyal, sandeepc@utexas.edu Q-DiffusionOursMixDQOursQ-DiTOurs Figure 1: Images generated by each per-architecture PTQ baseline and by Chameleon at 4-bit weights (W 4 A 8 ), from the COCO-2014 caption “An old city fire hydrant has ‘Love was found here’ painted on it.” ABSTRACT A very popular way to enable image generation on memory-constrained accelera- tors using modern spatiotemporal generative models is post-training quantization (PTQ). However, every existing diffusion PTQ scheme shares an unstated com- mitment: the number format is fixed in advance, and only the scale, zero point, or the per-layer bit-width is allowed to move. This is unfortunate, because at a fixed bit-width the best format depends on the distribution being encoded, and that distribution differs from tensor to tensor: across weight channels, across lay- ers, and – in a denoising model – along the diffusion timestep, where activations slide from heavy-tailed and noise-dominated at t → T to tightly clustered and structured at t → 0. One format for the whole network is therefore mispriced for most of its tensors, and re-tuning a scale cannot repair a format mismatch. In this work, we propose a PTQ framework, which we call Chameleon, that holds the bit-width fixed and treats the number format itself as a discrete vari- able, chosen per weight channel and per (layer, timestep bucket) activation tensor. Chameleon draws activation formats from a palette of INT8, FP8 E4M3, FP8 E5M2, MXFP8, MXINT8 and weight formats fromINT8, MXINT8 at 8 bits or INT4, NF4, FP4 E2M1, MXINT4, MXFP4 at 4 bits, choosing activation for- mats ahead of time from two cheap statistics – empirical activation kurtosis and closed-form diffusion SNR ̄α t /(1− ̄α t ) – stored in a per-(layer, timestep bucket) lookup table, and weight formats offline by reconstruction error. An architectural fork adapts the same selection layer to each model family, so each model exercises the palette as far as its own statistics warrant: weights and per-(layer, bucket) acti- vations on multi-step SDXL, weights alone where a single sampler step leaves no timestep axis. We evaluate Chameleon across three diffusion regimes – multi-step SDXL, single-step SDXL-Turbo, and the PixArt-α Diffusion Transformer – on COCO-2014. Chameleon achieves the best FID for all six backbone×bit-width settings, while preserving semantic alignment with the text prompts (CLIP within 0.24 of the FP16 reference in every setting, and the best of all quantized methods at W 4 A 8 ). Adapting the format, rather than only its scale, recovers distributional fidelity at 4-bit weights while holding prompt adherence at the FP16 level. 1 1 website§ code 1 arXiv:2609.33496v1 [cs.LG] 27 Sep 2026 Offline AnalysisLoad-Time Architectural ForkInference Execution Graphs Weight SNR (per-format round-trip) Adaptive Weight Palette argmax-SNR format search W8: INT8, MXINT8 W4: INT4, NF4, FP4, MX4 Timestep t Diffusion SNR(t) (no forward pass) Activation Statistics (Kurtosisκ, per layer × bucket) Per-(Layer × Timestep-Bucket) Activation Format LUT INT8, FP8, MX UNet Diffusion (Q-Diffusion style) Few-Step Distilled (SDXL-Turbo, MixDQ style) Diffusion Transformer (Q-DiT style) Fake-Quant Dispatch W: per-output-channel format A: per-bucket format, static scales + MXFP8 shortcut layers Fake-Quant Dispatch W: per-channel (8b), (g,f) (4b) A: MixDQ static scales (1-step) Fake-Quant Dispatch W: input-aware (g,f) search A: macro-route + per-tensor micro-scaling Few-Step Exception weights: adaptive palette feeds all three arms activations: format LUT feeds the multi-step arms only A single sampler step leaves no timestep axis to route over, so the few-step arm inherits MixDQ's calibrated static activation scales unchanged. Chameleon supplies only its weights. Routing Rule Applied per (layer, timestep bucket). shortcut layer → MXFP8 E4M3 κ > 5 or SNR < 0.2 → FP8 E5M2 κ ≤ 3 and SNR > 2 → INT8-asym otherwise→ FP8 E4M3 Shortcut rule is checked first, before any statistic. Figure 2: Chameleon framework: Offline, a one-pass calibrator accumulates per-(layer, bucket) activation moments for the empirical kurtosis κ l (t), while the diffusion SNR(t) is read from the noise schedule. The router applies the rule of Section 4.3 to both and writes the format into an integer lookup table F ∈ 0,..., 4 L×B (code 4 is unused); weights are selected offline (Sections 4.5 and 4.6). At inference, one fake-quantization module reads the LUT per layer per step on the multi- step paths and dispatches to the matching routine. 1INTRODUCTION The frontier of generative AI lies not in the cloud but on the edge (Zhou et al., 2025). Latent diffusion models, few-step distilled models, and diffusion transformers (DiTs) all generate images from pure noise by stepping through a learned vector field for tens to hundreds of forward passes through a network holding billions of parameters: SDXL alone has roughly 2.6 billion, and text encoding and the variational auto-encoder add another billion. Replacing 16-bit numerics with 8-, 6-, or 4-bit ones – post-training quantization (PTQ) – is the standard response, cutting memory footprint and latency while raising throughput (Nagel et al., 2021; Frantar et al., 2023; Xiao et al., 2023). This paper proposes a PTQ scheme for the iteratively denoising generators in that list. The key idea is that while weights can be statically quantized, activations should not be, because of the iterative nature of the inference pipeline. We call our dynamic format adapter framework Chameleon: at a fixed bit-width it chooses a number format per tensor – per weight channel, per layer, and per timestep bucket where a timestep axis exists – using cheaply computed statistical heuristics. Prior work has contributed a great deal to this space (Section 2), but the four diffusion PTQ baselines we compare against – Q-Diffusion, PTQ4DM, MixDQ and Q-DiT – all take quantization to mean rounding to the nearest INT8 format. This is suboptimal for at least two reasons. First, at a fixed bit-width the format is still free, and the right choice follows the distribution being encoded: Kuzmin et al. (2022) show that the signal-to-quantization-noise ratio (SQNR) at a given width is a function of both that distribution and the format, and Zhang et al. (2024) turn this into a per-layer INT-or-FP choice for LLMs. Tensors within one network differ in shape – across weight channels and across layers – so no single format is right for all of them. Denoising networks add a second axis: the activations of a single layer are themselves a parametric family of distributions indexed by timestep t (Li et al., 2023). At t → T , activation tensors are dominated by Gaussian noise, and the internal activations they induce are heavy-tailed, with kurtosis (κ) above 5; at t → 0 they are dominated by the structured signal of a near-convergence latent, with κ often below 3. The format that is right at t = 0 is wrong at t = T . Re-tuning the scale of INT8 cannot make it tolerate heavy tails, any more than re-scaling FP8 E5M2 can give its logarithmic bins the density to render fine texture. The fix is to change formats along the schedule. 2 Second, microscaling formats – MXFP8, MXINT8, MXINT4 (OCP Microscaling Formats Work- ing Group, 2023; Rouhani et al., 2023) – are now hardware features on Blackwell-class accelerators, with FP8 already native on Hopper and Ada. One shared 8-bit exponent per 32 elements lets a single tensor hold values spanning very different magnitudes without one global scale covering them all. This is exactly what the concatenations at every UNet shortcut need, where shallow skip features meet deep upsampled features. Measured on SDXL, the tensor entering a shortcut conv1 spans a peak-to-median per-channel range of 58× at the median layer and up to 163× (Appendix A.11), so one per-tensor scale must cover outliers that most channels never approach. Q-Diffusion split the computational graph for this; with MX formats, one need not. These two observations – that the right format depends on the tensor, and on t where a timestep axis exists, and that the format should sometimes be a microscaling block format – are the substance of this paper. Figure 2 sketches the resulting framework end-to-end. We present Chameleon, a PTQ framework that treats the number format as a discrete variable, chosen per weight channel and per (layer, timestep bucket) activation tensor from the palettes of Section 4.2. Two cheap statistics – the empirical kurtosis κ l (t) and the closed-form diffusion SNR – decide it offline, and the result costs one indexed read per layer per step. 1.1MOTIVATION PTQ research for time-stepped image generators is architecture-specific, but the three lines of work converge on one observation: the activation distributions inside a denoising network are non- stationary along the diffusion trajectory, and that non-stationarity is the dominant source of quantiza- tion error. What none of those four adjusts is the number format itself. Q-Diffusion, PTQ4DM, MixDQ, and Q-DiT all commit up-front to a single format – invariably INT8 – and route their design effort into scales, zero points, per-layer bit-widths, group sizes, and sampler schedules on top of that fixed commitment. This is an odd restriction to accept when the underlying activation family spans regimes as different as heavy-tailed, noise-dominated activations at t→ T and tightly clustered structured signals at t → 0. If the family of activation distributions is the problem, the family of number formats is the natural response. Chameleon respects those architecture-specific lessons rather than discarding them: a hard fork at model load selects a UNet, few-step, or DiT execution path (Section 4.6), and because the format choice sits underneath that machinery, each path threads Chameleon’s LUT through the treatment inherited from prior work. “Which format to use” is thereby decoupled from “which architecture we are quantizing.” This is tractable because the format is a discrete variable: the palette is small (five formats for activations, six for weights at 4 bits) and fixed by what accelerators implement natively, so selection is a routing problem rather than a continuous optimization, and both statistics that decide the per- tensor Mean Squared Quantization Error (MSQE) comparison are cheap – kurtosis is a one-pass moment accumulation, and SNR is read off the noise schedule with no forward pass. 2RELATED WORK Extended versions of the paragraphs below, and a note on LLM quantization, are in Appendix A.1. Diffusion-model PTQ: Q-Diffusion (Li et al., 2023) first recognized that activation distribu- tions inside a denoising UNet are not stationary across the schedule, answering with a uniform- timestep calibration sampler and a split quantizer for the shortcut layers. PTQ4DM (Shang et al., 2023) added per-bucket calibration statistics. Both take the format itself – INT8 – as a given and tune scales around it. Few-step and consistency-model PTQ: Few-step distilled models – by consistency (Luo et al., 2024) or adversarial (Sauer et al., 2024) distillation – are hostile to quantization: each of their one to four steps carries far more of the semantic burden than one step of a 50-step trajectory. MixDQ (Zhao et al., 2024) combines metric-decoupled mixed precision, assigned by integer programming, with a BOS-aware bypass in the cross-attention K and V projections; Q-Sched (Frumkin & Marculescu, 2026), concurrent with and complementary to Chameleon, instead learns a single pair of scalar 3 preconditioning coefficients that warp the sampling trajectory. Our few-step fork composes with MixDQ rather than replacing it (Section 4.6). DiT quantization: Diffusion transformers exhibit large variance across the input channel dimen- sion of their linear-layer activations, which tensor- or output-channel-wise quantization cannot ab- sorb. Q-DiT (Chen et al., 2025a) introduced group-wise weight quantization with an evolution- ary search over group sizes g ∈ 32, 64, 128, 192, 288, and dynamic on-the-fly scale and zero- point computation for activations – again with INT as the only number system. ViDiT-Q (Zhao et al., 2025) reports W 8 A 8 and W 4 A 8 on PixArt-α with finer-grained dynamic quantization, again within INT. Our DiT fork keeps both, generalizing the group search to a joint (g,f ) search over group size and format (Section 4.6). PTQ4DiT (Wu et al., 2024), FP4DiT (Chen et al., 2025b) and ViDiT-Q are not re-run in our harness and so do not appear in Table 1 (Appendix A.1). Microscaling formats: The OCP MX specification (OCP Microscaling Formats Working Group, 2023; Rouhani et al., 2023) standardized block-shared-exponent narrow formats: each block of 32 elements carries one shared 8-bit exponent, absorbing intra-tensor magnitude variation without per-channel scale infrastructure. To our knowledge, Chameleon is the first PTQ scheme for diffusion models to use MX formats adaptively, routing concatenation-bearing UNet shortcut layers to MXFP8 by topology. Format selection beyond INT: At a fixed bit-width the format is itself a free variable: MoFQ (Zhang et al., 2024) chooses INT or FP per layer for LLMs by quantization error, and So et al. (2023a) search a per-tensor floating-point encoding, layer by layer, for diffusion. TDQ (So et al., 2023b) comes closest to our temporal axis, but varies the quantization interval with t, not the format (Appendix A.1). Where we sit: Chameleon is the first PTQ scheme for time-stepped image generators to treat the number format as a discrete variable indexed by (layer, timestep bucket) – per-layer format selection at a fixed width was introduced for LLMs (Zhang et al., 2024), and timestep-dependent quantization parameters for diffusion (So et al., 2023b), but not the format along the schedule – and the first to demonstrate the same routing principle across UNet, few-step UNet, and image DiT under one framework. It is composable rather than competitive: where existing methods care about scales (Q-Diffusion, PTQ4DM), bit-widths (MixDQ), group sizes (Q-DiT), or sampling trajectories (Q-Sched), Chameleon cares about formats, and the underlying calibration loop and group search from each of these methods can sit on top of it without modification. 3BACKGROUND & PRELIMINARIES 3.1DIFFUSION BASICS In the variance-preserving discretization used by Stable Diffusion and its derivatives, the noise schedule is summarized by the cumulative product ̄α t = Q s≤t (1− β s ), and the signal-to-noise ratio admits the closed form SNR(t) = ̄α t 1− ̄α t ,(1) which falls monotonically in t across five to eight orders of magnitude along the schedule. We use it as one of our two routing statistics: it is known at calibration time and costs nothing to evaluate. Appendix A.2 gives the continuous-time formulation, the per-model SNR ranges, and how DiTs and few-step models fit the same picture. 3.2ASYMMETRY IN THE STATISTICS OF WEIGHTS VS. ACTIVATIONS A trained denoising network is a static set of weights W l , whose statistics do not depend on t and can be characterized once, offline, per channel. Activations are different: for a fixed layer l, the input tensor x l (t) depends on both the random latent and the timestep, and its distribution changes dramatically along the schedule. Appendix A.3 works through an illustrative example on SDXL: measured along the schedule, activation kurtosis and SNR(t) separate three phases – heavy-tailed at 4 low SNR (Phase 1), settling at mid SNR (Phase 2), and near-Gaussian at high SNR (Phase 3) – each best served by a different format, and layers cross them at different times, which is why Chameleon routes per (layer, bucket) rather than per bucket alone. 4THE CHAMELEON FRAMEWORK 4.1PROBLEM STATEMENT Let N be a denoising network with quantizable layers l = 1,...,L. For each layer let X l (t) ∈ R C 1 ×C 2 ×· denote the input activation tensor at timestep t and W l ∈ R C out ×C in ×· the weight tensor. We discretize the schedule into B uniform-width buckets indexed b = 0,...,B − 1 and write b(t) for the bucket containing t. Given a finite paletteF of number formats – each with its own scaling granularity g (per-tensor or per-block for activations, per-output-channel or grouped for weights; Section 4.6 fixes this per archi- tecture) – we seek for each (layer l, bucket b) the format minimizing the mean-squared quantization error f ⋆ l,b = arg min f∈F E t∈b h X l (t)− DQ f Q f (X l (t)) 2 2 i ,(2) where Q f and DQ f are the quantization and de-quantization operators of format f at its native granularity g. The analogous objective is solved per output channel for weights, with the expectation over t dropped because weights are static. Solving equation 2 exhaustively means materializing X l (t) and computing five round-trips per (layer, bucket). That is feasible for one calibration pass, but two cheap scalars – the empirical kur- tosis κ l (t) of X l (t) and the diffusion SNR of equation 1, which depends on t alone – approximate the argmin well enough to populate a static lookup table that ships with the model. 4.2FORMAT PALETTE The activation palette is F a = INT8-asym, FP8 E4M3, FP8 E5M2, MXFP8 E4M3, MXINT8, indexed by integer codes 0, 1, 2, 3, 4 in the runtime LUT. The first three are conventional per-tensor formats; the last two are microscaling formats with block size 32 and a shared 8-bit exponent. The weight palette is bit-width dependent: F (8) w = INT8-sym, INT8-asym, MXINT8, F (4) w = INT4-sym, INT4-asym, NF4, FP4 E2M1, MXINT4, MXFP4 E2M1. F (4) w above is the full 4-bit palette; each architectural fork searches a subset of it (Section 4.6), and Appendix A.11 describes each code. We keep the palette small: the MSQE landscape has clear plateaus (Phases 1–3 of Appendix A.3), and extra formats inside a plateau buy nothing while inflating the LUT. MXINT8 is defined in the activation code space for symmetry with the weight palette but is never selected by the routing rules of Section 4.3; the remaining four are the smallest set covering all three phases plus the concatena- tion case. Alternatives to plain integer and floating-point coding exist in the broader compression literature (Sanyal et al., 2020; Johnson, 2018), but we restrict the palette to formats that map onto upcoming hardware; Appendix A.11 describes each. 4.3ROUTING THRESHOLDS For each (layer, bucket) pair we apply the decision rule below, which approximates the argmin of equation 2 under a generalized-Gaussian model. UNet shortcut layers are pinned by topology before 5 any statistic is consulted; the rest are routed by κ and SNR: If l is a UNet shortcut layer: f ⋆ l,b = MXFP8 E4M3(shortcut concatenation) Else if κ l (t) > 5 or SNR(b) < 0.2 : f ⋆ l,b = FP8 E5M2(Phase 1, heavy tails) Else if κ l (t)≤ 3 and SNR(b) > 2 : f ⋆ l,b = INT8-asym(Phase 3, clean signal) Else: f ⋆ l,b = FP8 E4M3(Phase 2, settling) Here SNR(b) ≡ SNR(t b ), evaluated at the bucket midpoint t b = bT/B + T/(2B), as in Algo- rithm 1. The SNR gate overrides kurtosis by design: below τ low every non-shortcut layer is routed to FP8 E5M2 (Table 7), so per-layer routing acts in the mid- and high-SNR buckets. The constants (κ low ,κ high ) = (3, 5) and (τ low ,τ high ) = (0.2, 2.0) are fixed a priori rather than tuned per model: the kurtosis gates are where the per-format MSQE curves cross under a generalized-Gaussian model, and the SNR gates mark the macroscopic phases of the noise schedule. Empirically, the routing is insensitive to their exact values: shifting the kurtosis gates from (3.0, 5.0) to (3.5, 5.5) – +17% and +10% respectively – changes FID by 0.02, below the 0.04 run-to-run variation we observe between two independent calibrations of an identical configuration (Appendix A.9). 4.4CALIBRATION: LOCKSTEP SAMPLING AND LUT CONSTRUCTION Calibration runs as a single pass on top of a Q-Diffusion-style uniform timestep sampler. We collect 128 prompts (COCO captions), bucket the schedule into B = 10 uniform-width windows, and generate one 20-step trajectory per prompt. During each forward pass, every Chameleon- instrumented layer accumulates running statistics into an L× B table, pooling the conditional and unconditional halves of each classifier-free-guidance batch; Algorithm 1 in the supplement gives the full pseudocode. The accumulator stores raw power sums (n, P x, P x 2 , P x 3 , P x 4 ) plus a running min and max, from which κ l (t) follows in closed form. Memory is O(1) in the number of prompts – seven scalars per (layer, bucket) – so SDXL’s 372 quantized layers at B = 10 need 26,040 scalars, about 200 KB. 4.5PER-CHANNEL WEIGHT SELECTION Weights are static, so their format selection runs offline and at finer granularity. For each output channel c of each conv or linear, we round-trip W l [c, :,...] through every format in the appropriate palette and pick the format with the highest quantization signal-to-noise ratio (SQNR) in dB: f ⋆ l,c = arg max f∈F w 10 log 10 E W l [c] 2 E h W l [c]− DQ f (Q f (W l [c])) 2 i .(3) The per-channel grain matters: even within one SDXL conv layer, the kurtosis of weights along the output-channel axis varies enough that a tensor-wise choice would force a compromise no channel benefits from. It costs one byte of format metadata per output channel, about 1 MB across the UNet. 4.6THE ARCHITECTURAL FORK A model loader inspects the network topology once and dispatches to one of three execution paths. The fork is the only branch in the framework; everything downstream is shared. UNet diffusion path (SDXL): Activations follow Section 4.3 with static, ahead-of-time-calibrated scales (Q-Diffusion style). Layers matching the regex upblocks. * .resnets. * .conv1 – the conv layers immediately downstream of a shortcut concatenation – are unconditionally routed to MXFP8 E4M3, bypassing the κ/SNR check, because their inputs are wide-tailed in a way that no per-tensor format can absorb. Weights follow Section 4.5. Few-step path (SDXL-Turbo): A one-step schedule has no timestep axis to route over, so this path inverts the division of labor: Chameleon owns the weights and inherits the activations 6 wholesale. Activations use MixDQ’s calibrated static per-tensor scales together with its metric- decoupled mixed-precision assignment, unchanged. Weights are replaced by Chameleon’s adap- tive palette – per-channel SQNR selection over F (8) w at 8 bits, and a per-layer (g,f ) search over 32, 64, 128, 192, 288×INT4-asym,NF4,FP4 E2M1,MXINT4,MXFP4 E2M1 at 4 bits (the MX formats carry one power-of-two scale per 32-element block, so g does not change them and they are searched at g = 32) – substituted for MixDQ’s symmetric fold at the point where the quan- tized weight tensor materializes (the nine up-block conv shortcut layers stay FP16 at both bit-widths; Appendix A.4). The weight palette alone therefore accounts for the improvement over MixDQ at both bit-widths, and MixDQ’s BOS-aware bypass becomes unnecessary under it (Ap- pendix A.9), which also removes its batch-size-one inference constraint. DiT path (PixArt-α): The MX shortcut logic is dropped – DiTs do not have shortcut concate- nations of the kind UNets do. Two changes replace the shortcut rule: (i) Weights use a joint (g,f ) search. For each linear layer we evaluate the SQNR – input-aware at 4 bits, i.e. weighting each input channel’s error by its activation energy E[x 2 i ] – of every (g,f ) ∈ 32, 64, 128, 192, 288×INT4-asym,NF4,FP4 E2M1 tuple and pick the argmax. The search is restricted to the non-MX members of F (4) w , since a searched g already supplies the block granularity MX would contribute. Groups run along the input-channel dimension, following Q-DiT’s observation that this is where DiT activations have their dominant variance. (i) Activations use macro-routing with dynamic per-sample scaling: the format choice f ⋆ l,b from the LUT (equation 2) is the macro decision, but the scale is computed dynamically from the current sample’s range at inference rather than read from a calibrated table. This follows Q-DiT’s obser- vation that DiT activations shift drastically across samples. Applied unchanged to PixArt-α, this rule produces a markedly different assignment from the UNet’s. At both bit-widths, FP8 E5M2 wins in 97–100% of the 282 quantized linears in every bucket and INT8-asym is never selected, so the three-phase progression of Appendix A.3 does not appear here. Since SNR(b) is large in the cleanest buckets, the gate that fires must be κ l (t) > 5: DiT activations stay heavy-tailed along the entire schedule. The thresholds are identical across both architectures, with no per-model tuning, yet they track the architecture rather than reproducing the UNet’s answer. 4.7IMPLEMENTATION AND RUNTIME The runtime path is a single n.Module inserted before each quantizable layer; Algorithm 2 gives the pseudocode and Appendix A.7 two reproducibility notes (LUT buffer registration and FP8 range clamping). Here we say how our MX numbers should be read. MX block formats are simulated by reshaping to blocks, computing the shared exponent, round- tripping each element, and reshaping back. The activation path follows the OCP specification ex- actly: the shared scale is the power-of-two 2 ⌊log 2 max i |x i |⌋ (an E8M0 exponent), so the simulation matches conforming MX hardware. The SDXL weight-side implementation instead uses an uncon- strained per-block scale, which is strictly more expressive than the specification allows (the few-step path’s MX weights already use power-of-two scales, and the DiT path selects no MX weight format); the numbers we report for MX weight formats should be read accordingly. Appendix A.12 mea- sures what conformance would cost and how it changes the palette. We report fake-quant numbers throughout because real INT8/FP8/MX kernels are not yet uniformly available across the architec- tures we evaluate; on Blackwell we expect native kernels (e.g., Microsoft’s microxcaling) to remove the simulation overhead. The whole framework is roughly 5.8 kLOC of PyTorch. We will release the code and the per-model LUTs that reproduce Section 5 exactly. 5EXPERIMENTS 5.1SETUP We quantize SDXL base 1.0 (Podell et al., 2024), SDXL-Turbo (Sauer et al., 2024), and PixArt-α XL/2 1024-MS (Chen et al., 2024) through the UNet, few-step, and DiT paths of Section 4.6, and 7 re-run each family’s prior PTQ schemes through one shared harness with identical prompts, seeds, and scoring. We report clean-FID (Parmar et al., 2022) over 24,576 COCO-2014 validation captions (Lin et al., 2014) and CLIP-score (Radford et al., 2021) as a prompt-adherence check; resolutions and samplers differ per family (Table 1), so FID is comparable within a backbone but not across. All runs use fake quantization on a single A100, so we report quality and calibration cost but not latency. Appendix A.4 gives the full setup. Table 1: Combined evaluation on COCO-2014 (24,576 prompts, one image per caption). Clean- FID is computed against the full val2014 set and CLIP-score (ViT-L/14, cosine ×100) against the matching captions; best FID per backbone (and CLIP for W 4 A 8 ) in bold. * Ours. In both SDXL-Turbo rows the nine up-block conv shortcut layers stay FP16 (Section 4.6). SetupMethodBitsFID↓CLIP↑ SDXL (50 steps, CFG 7.5, 1024× 1024) FP16 baselineW 16 A 16 16.1626.88 Q-DiffusionW 8 A 8 14.7026.77 PTQ4DMW 8 A 8 14.6526.68 Chameleon * W 8 A 8 14.2326.70 Q-DiffusionW 4 A 8 21.4126.27 PTQ4DMW 4 A 8 21.8226.21 Chameleon * W 4 A 8 14.4326.64 SDXL-Turbo (1 step, no CFG, 512× 512) FP16 baselineW 16 A 16 21.6326.63 MixDQW 8 A 8 21.4326.64 Chameleon * W 8 A 8 20.9326.62 MixDQW 4 A 8 24.5025.88 Chameleon * W 4 A 8 21.2926.85 PixArt-α (20 steps, CFG 4.5, 1024× 1024) FP16 baselineW 16 A 16 27.6325.99 Q-DiTW 8 A 8 27.6925.99 Chameleon * W 8 A 8 24.3325.81 Q-DiTW 4 A 8 23.5325.73 Chameleon * W 4 A 8 22.2426.09 5.2MAIN RESULTS Table 1 reports the headline numbers for the three backbones. In SDXL, Chameleon reaches 14.23 FID at W 8 A 8 and 14.43 at W 4 A 8 , against FP16 16.16 and the best prior results of 14.65 (PTQ4DM) and 21.41 (Q-Diffusion); the 7.0-point margin at 4 bits is the largest in the table. CLIP slips from 26.88 to 26.70 and 26.64, the latter the best of any quantized method by 0.37. Both configurations share the same A 8 routing, so the 0.20 FID difference is attributable to the weight palette alone. In SDXL-Turbo, FID improves from 21.63 in FP16 to 20.93 (W 8 A 8 ) and 21.29 (W 4 A 8 ), with CLIP holding at 26.62 and rising to 26.85, the latter 0.22 above the FP16 reference. Because this fork inherits MixDQ’s activations unchanged, the margin over MixDQ – 0.50 FID at 8 bits, 3.21 at 4 bits – isolates the weight palette: the tighter the weight budget, the more a per-channel format choice buys. In PixArt-α, Chameleon reduces FID from 27.63 to 24.33 at W 8 A 8 and 22.24 at W 4 A 8 , beating Q-DiT by 3.36 and 1.29 respectively, and exceeding its CLIP by 0.36 at 4 bits. On the weight side the difference is the joint (g,f ) search: at 8 bits it settles on INT8-asym everywhere but at g = 32 rather than Q-DiT’s 128 (MXINT8 is never selected), and at 4 bits on g = 32 throughout, with NF4 – unavailable to an INT-only baseline – for 69 of the 282 linears. Which axes the palette uses differs by backbone, as the statistics dictate: SDXL uses all of them (per-channel weights, per-layer activations, three temporal regimes, the topological MXFP8 pin); PixArt-α uses the weights and a near-uniform activation assignment (FP8 E5M2 in 97–100% of linears); SDXL-Turbo, whose single step leaves no timestep axis, uses the weight palette alone. 8 Appendix A.9 separates the activation axes on SDXL: against the best single fixed format, the per- layer choice is worth 0.82 FID and the timestep axis a further 0.12. Two patterns hold across all three backbones. Every Chameleon configuration scores FID below its FP16 reference, and on SDXL and PixArt-α the 4-bit model is competitive with or better than the 8-bit model. We do not have a validated account of either: a low-pass explanation holds on PixArt-α but not on the UNets, as we discuss in Appendix A.8 of the supplement. A qualitative comparison at W 4 A 8 is provided in Figure 5 in Appendix A.10. 5.3CALIBRATION COST Chameleon’s calibration involves no gradient updates, no auxiliary networks, and no integer pro- gram of our own – the few-step path excepted, and only because it consumes MixDQ’s precomputed mixed-precision assignment unchanged. Calibration takes at most 45 minutes on a single A100 (45 minutes for SDXL, 7 for PixArt-α and 1 for SDXL-Turbo) and under an hour for all three back- bones combined (Table 2 in Appendix A.7). The routing hyperparameters – the kurtosis and SNR thresholds and the bucket count B – are fixed across every model, with no per-model tuning; only the palette is specialized per architecture, and structurally so (Section 4.6). 6DISCUSSION & LIMITATIONS Our numbers come from fake quantization rather than real low-precision kernels, so we make no efficiency claims: they characterize what the format assignment costs in fidelity, and measuring its latency and memory savings on native FP8 and MX kernels remains future work. The evalua- tion is limited to image generation; extending the routing to video DiTs, whose temporal-attention sensitivities are uncharacterized, is a natural next step, and sub-4-bit (W 2 /W 1 ) regimes would re- quire quantization-aware training rather than PTQ. The palette also assumes its formats exist in hardware: FP8 and MX need Hopper- or Blackwell-class support, and on INT-only NPUs it re- duces to its INT members. Per-channel mixed formats likewise do not map to one native GEMM tile; they would run as same-format sub-GEMMs after a channel permutation, or with weights de- quantized in registers as existing W 4 A 8 kernels do. Appendix A.13 expands these points, adding the per-channel format-metadata overhead at extreme model scale and calibration generalization to out-of-distribution prompts. 7CONCLUSION We argued that at a fixed bit-width the number format is not a design constant but a discrete variable, and that it should be chosen per tensor: per weight channel, per layer, and – where a timestep axis exists – per timestep bucket. The argument is structural: a format is priced for a distribution, and the distributions inside a denoising network differ across channels, across layers, and along the schedule, sliding from heavy-tailed, noise-dominated tensors at t → T to tightly clustered, structured signals at t→ 0, so no single format in the standard 8-bit palette is correctly priced for all of them. Tuning scales cannot fix a format mismatch. Chameleon makes that choice adaptive. Two ahead-of-time statistics – empirical kurtosis and the closed-form diffusion SNR – populate a format lookup table that the runtime indexes with one ten- sor read, and a single architectural fork specializes the routing to UNet, few-step, and DiT back- bones. Across all three backbones and both bit-widths, the resulting quantized configurations re- duce FID below the FP16 reference while holding CLIP-score within 0.24 of it, and lead every quantized baseline on CLIP at W 4 A 8 (Table 1). 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URL https: //arxiv.org/abs/2505.02256. 13 SUPPLEMENTARY MATERIALS Table of Contents Appendix A.1Extended Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 A.2Diffusion Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 A.3Activation Phases for SDXL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 A.4Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17 A.5Architectural-Fork Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19 A.6CLIP-Score Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19 A.7Algorithm Pseudocode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20 A.8On Chameleon FID below the FP16 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21 A.9Ablations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22 A.10 Qualitative Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25 A.11 Number-Format Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25 A.12 MX Conformance and Its Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 A.13 Extended Discussion and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 Statements B.1AI Use Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 B.2Ethics Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 B.3Reproducibility Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 14 AAPPENDIX A.1EXTENDED RELATED WORK Diffusion-model PTQ: Q-Diffusion (Li et al., 2023) was the first PTQ scheme to recognize that the activation distributions inside a denoising UNet are not stationary across the diffusion sched- ule. Their fix has two parts: a uniform-timestep sampler during calibration that visits the entire schedule rather than a single timestep, and a split quantizer for the UNet’s shortcut layers, which separately quantize the deep and shallow halves of the concatenated tensor before applying a fused matmul. PTQ4DM (Shang et al., 2023) sharpened the timestep handling by partitioning the schedule into buckets and accumulating per-bucket calibration statistics, but kept the format fixed at INT8. Both methods take the format itself as a given and tune scales around it. Two later lines of work stay within INT but attack the error differently: PTQD (He et al., 2023) models the quantization error as correlated noise and corrects it during sampling, while EfficientDM (He et al., 2024) recovers low-bit quality by fine-tuning LoRA weights, which places it closer to QAT than to PTQ. Few-step and consistency-model PTQ: Few-step distilled models – whether obtained by consis- tency distillation, as in Latent Consistency Models (Luo et al., 2024), or by adversarial distillation, as in SDXL-Turbo (Sauer et al., 2024) – are particularly hostile to quantization, because each of their one to four denoising steps carries a much larger fraction of the total semantic burden than a single step in a 50-step DDIM trajectory; quantization noise that an iterative model would absorb statistically becomes visible in the output. MixDQ (Zhao et al., 2024) addressed this by combining metric-decoupled mixed precision – separately measuring image-quality and text-alignment sen- sitivity per layer and assigning bit-widths via integer programming – with a surgical BOS-aware quantization (BAQ) that exempts the begin-of-sentence position of the text embedding from acti- vation quantization in the cross-attention K and V projections, substituting a pre computed FP16 output. Q-Sched (Frumkin & Marculescu, 2026) takes a different route, leaving the quantized weights frozen and learning a single pair of scalar preconditioning coefficients, applied to the latent and to the quantized noise prediction at every step, that warps the integration trajectory to compen- sate for the quantization-induced drift in the vector field. Our few-step fork applies Chameleon’s weight palette over MixDQ’s calibrated activation pipeline, leaving the activation side entirely to MixDQ: with a single denoising step the timestep axis degenerates, so the routing of Section 4.6 applies to weights only; notably, its BOS-aware bypass becomes unnecessary under Chameleon’s weight palette – re-enabling a faithful equivalent changes FID by less than 0.15 (Appendix A.9) – which also lifts MixDQ’s batch-size-one inference constraint. Q-Sched is concurrent with and complementary to Chameleon. DiT quantization: Diffusion transformers exhibit large variance across the input channel dimen- sion of their linear-layer activations rather than output channels, which means standard tensor or output-channel-wise quantization underflows the small-magnitude channels and crushes the model. Q-DiT (Chen et al., 2025a) introduced group-wise weight quantization with an evolutionary search over group sizes g ∈32, 64, 128, 192, 288, and dynamic on-the-fly scale and zero-point computa- tion for activations because pre-calibrated scales drift unacceptably across samples. Q-DiT, again, fixes INT as the only number system. Our DiT fork keeps Q-DiT’s group search and dynamic micro-scaling, but generalizes the search space from group-only to (g,f ) joint over group size and format choice fromINT4, NF4, FP4 at 4 bits orINT8 sym, INT8 asym, MXINT8 at 8 bits. PTQ4DiT (Wu et al., 2024) instead balances channel salience to reach W 4 A 8 on DiTs, and FP4DiT (Chen et al., 2025b) quantizes PixArt-α with floating-point rather than integer formats at W 4 A 6 . Neither they nor ViDiT-Q (Zhao et al., 2025) are re-run in our harness, so Table 1 compares against the per-architecture baseline each family established. Microscaling formats: The OCP MX specification (OCP Microscaling Formats Working Group, 2023; Rouhani et al., 2023) standardized a family of block-shared-exponent narrow formats – MXFP8, MXINT8, MXFP6, MXFP4, MXINT4 – in which each block of 32 elements carries one shared 8-bit exponent and the elements themselves are stored in a narrow integer or floating-point body. Our fake-quantization implements it directly in PyTorch (Section 4.7). The hardware payoff is that the shared exponent absorbs intra-tensor magnitude variation without any per-channel scale infrastructure. To our knowledge, Chameleon is the first PTQ scheme for diffusion models to use MX formats adaptively, routing concatenation-bearing UNet shortcut layers to MXFP8 by topology. 15 LLM quantization, in passing: GPTQ (Frantar et al., 2023), AWQ (Lin et al., 2024) and SmoothQuant (Xiao et al., 2023) established the modern playbook for LLM PTQ, and SmoothQuant’s idea of migrating activation outliers into the weight space inspired several dif- fusion follow-ups. Edge-deployment-oriented variants such as EntroLLM (Sanyal et al., 2026) compose entropy-coded weight compression on top of post-training quantization to cut bandwidth on resource-constrained devices. Format selection at a fixed bit-width also originates in this line: MoFQ (Zhang et al., 2024) chooses INT or FP per layer by quantization error for LLMs, and defers finer granularity to future work. Chameleon inherits that idea and extends it along three axes – the timestep, a palette that includes NF4 and the MX formats, and the architectural fork – none of which has a counterpart in LLM quantization, where the temporal structure Chameleon exploits is absent. A.2DIFFUSION BASICS This appendix expands Section 3.1. A continuous-time forward diffusion is the SDE dx t = μ(x t ,t) dt + σ(t) dw t ,(4) which gradually corrupts a clean sample x 0 ∼ p data into Gaussian noise x T ∼ N (0,I). Sampling is performed by integrating the corresponding reverse-time probability-flow ODE dx t = μ(x t ,t)− 1 2 σ(t) 2 ∇ x logp t (x t ) dt,(5) with the score given by a learned noise predictor, ∇ x logp t (x t ) ≈ −ε θ (x t ,t)/ √ 1− ̄α t . The variance-preserving discretization and the closed-form SNR(t) of equation 1 are given in the main text; SNR(t) falls monotonically across five to eight orders of magnitude along the schedule; for SDXL’s scaled-linear discretization it runs from ∼ 10 3 at t = 0 to ∼ 10 −2 at t = T , and for PixArt-α’s linear schedule from∼ 10 4 to∼ 10 −4 . For a diffusion transformer (DiT) the architecture changes – convolutional UNet blocks become stacks of self-attention and feed-forward layers – but the temporal structure of the activations is the same. Few-step distilled models collapse the schedule to one to four sampler steps; each step is still indexed by an SNR value, but at a single sampler step (SDXL-Turbo) the timestep axis degenerates and Chameleon’s routing applies to weights only (Section 4.6). A.3ACTIVATION PHASES FOR SDXL This appendix gives an illustrative worked example of the activation statistics summarized in Sec- tion 3.2. Concretely, we instrument a fully trained SDXL UNet, run 128 calibration prompts through a 20-step denoising schedule, and record the empirical sample kurtosis κ l (t) = E[(x l − μ l ) 4 ] (E[(x l − μ l ) 2 ]) 2 (6) for the input activations of each of the 372 quantized convolution and linear layers – attention Q/K/V projections and the stem/head convolutions are kept in FP16 and excluded – at each of ten timestep buckets. Together with the diffusion signal-to-noise ratio SNR(t), three patterns emerge consis- tently across the instrumented layers and define the regimes Chameleon routes between. Table 7 (Appendix A.9.5) reports the per-bucket format distribution behind the percentages quoted below, and Table 3 ablates the two statistics that separate the phases. Phase 1 (low SNR, t → T ): κ l (t) > 5 for the majority of layers. Although the network input is dominated by the additive Gaussian noise √ 1− ̄α t ε – whose kurtosis is exactly 3 – the internal ac- tivations are markedly heavy-tailed: normalization layers and attention rescale the noise-dominated features unevenly, producing sparse large outliers. INT8 uniform quantization underperforms here because those outliers force the scale wide and the central bins go empty; the calibrated router assigns FP8 E5M2 to 97% of layers in the final bucket. Phase 2 (mid SNR): As coarse structure forms, κ l (t) settles into the range [3, 5] for most layers. The distribution still has tails that INT8 handles poorly, but the dynamic range has tightened by an order of magnitude. FP8 E4M3, with three mantissa bits and a±448 range, is the closest match, and becomes the modal choice (61% of layers in the mid buckets). 16 Phase 3 (high SNR, t → 0): Activations are now dominated by the structured signal; the dis- tribution narrows toward Gaussian for the bulk of layers. INT8, with its 256 uniform bins, is the highest-density 8-bit representation and overtakes the FP8 formats in per-format MSQE where both routing gates clear – κ l ≤ 3 and SNR(t) > 2 – which occurs for roughly one layer in ten in the cleanest bucket; E4M3 remains the plurality format elsewhere. The transitions are not synchronous across layers – early-resolution convolution blocks reach Phase 3 sooner than mid-block projection layers – which is why the routing decision is made per (layer, bucket) and not per bucket alone. A.4EXPERIMENTAL SETUP Section 5.1 of the main paper summarizes the setup; the full version follows. Models: We evaluated three publicly available pre-trained image generation models, none of which are fine-tuned: Stable Diffusion XL (SDXL) base 1.0 (Podell et al., 2024), SDXL-Turbo, a one-step adversarially distilled variant of SDXL (Sauer et al., 2024), and PixArt-α XL/2 1024-MS (Chen et al., 2024). SDXL uses the UNet path of Section 4.6; SDXL-Turbo uses the few-step path, which applies Chameleon’s adaptive weight palette on top of MixDQ’s calibrated static activations; PixArt-α uses the image DiT path. Dataset: All runs use the COCO-2014 validation set (Lin et al., 2014): we generate 24,576 im- ages, one per caption sampled from captions val2014.json, and compute clean-FID (Par- mar et al., 2022) against the full val2014 set and CLIP-score (ViT-L/14) against the matching captions (Radford et al., 2021). 2 Reference Point: For each backbone, we report the unquantized FP16 model as reference and compare Chameleon at W 8 A 8 and W 4 A 8 against the per-architecture prior PTQ schemes: Q-Diffusion (Li et al., 2023) and PTQ4DM (Shang et al., 2023) for SDXL, MixDQ (Zhao et al., 2024) for SDXL-Turbo, and Q-DiT (Chen et al., 2025a) for PixArt-α. These methods are sur- veyed in Section 2 and serve as the inspiration for the architectural fork of Section 4.6; for the head-to-head comparison in Table 1 we additionally re-run each of them through our shared evalua- tion harness, with an identical prompt set, seeds, and scoring pipeline. Few-step quantization coverage: Both the MixDQ baseline and Chameleon’s few-step path run through MixDQ’s released pipeline in fake-quantization mode. In that mode the pipeline quantizes only layers whose input is not split: the nine up-block conv shortcut layers, which MixDQ would otherwise split-quantize at the concatenation boundary (1280/640/320 decoder channels), keep FP16 weights and activations at both W 8 A 8 and W 4 A 8 , although MixDQ’s mixed-precision configuration assigns them bit-widths. Chameleon’s weight palette is applied at the same point in the pipeline as MixDQ’s weight fold and so does not reach these layers either. The exception applies identically to both rows, so the few-step comparison in Table 1 is like-for-like, but each few-step configuration carries these nine additional FP16 layers. Hardware: All runs use a single NVIDIA A100 80 GB. Calibration and inference are both per- formed in fake-quant (simulated quantization in FP16 arithmetic); we therefore report image qual- ity only, and omit inference latency and peak-memory numbers, which would reflect the simulation rather than a real-kernel deployment. Calibration cost is a property of the method rather than of the deployment, so we do report it (Table 2). Hyperparameters: B = 10 timestep buckets, 128 calibration prompts, no gradient updates any- where. Inference uses published step counts and native resolutions: SDXL at 50 steps with CFG 7.5 at 1024× 1024, SDXL-Turbo at 1 step with guidance disabled (CFG 0) at 512× 512, and 2 CLIP-score is reported as cosine similarity× 100, following convention, so the values in Table 1 corre- spond to cosine similarities of 0.257–0.269 and are directly comparable to numbers reported elsewhere in the text-to-image literature. Scores are computed with ViT-L/14 against the caption each image was actually generated from; Appendix A.6 documents the scoring path. We treat FID as the primary metric and CLIP as a prompt-adherence check, since CLIP measures text–image alignment rather than distributional fidelity. 17 PixArt-α at 20 steps with DPM-Solver (Lu et al., 2022) and CFG 4.5 at 1024× 1024. Because resolutions and samplers differ per family, FID magnitudes are comparable within a backbone but not across backbones. Seeds are fixed at the global-index level so every method generates the same prompt set. DownBlock2D (320 ch) CrossAttnDownBlock2D (640 ch) CrossAttnDownBlock2D (1280 ch) CrossAttnUpBlock2D (1280 ch) CrossAttnUpBlock2D (640 ch) UpBlock2D (320 ch) Mid block cross-attn, 1280 ch Noisy VAE latent, 4 × 128 × 128 conv_inconv_out Predicted noise (epsilon-hat) FP16FP16 Timestep t Size / crop ids Time + added embedding (t, pooled text, size/crop) CLIP text embedding (2048-d) text encoders (FP16) c conv1 ×3 c conv1 ×3 c conv1 ×3 timestep conditioning pooled text K/V A₈ Activation Quantization (Runtime) Macro-routing, static scales share of the 372 layers per format, per bucket Timestep BucketFormat Code BucketINT8E4M3E5M2 T110%50%37% T212%48%37% T312%49%37% T4–61%36% T5–62%35% T6–62%36% T7–98% T8–98% T9–98% T10–98% clean signal (low t) pure noise (high t) MXFP8: the 9 shortcutconv1(2.4%) in every bucket per-bucket scales, calibrated ahead of time and static at inference (Q-Diffusion style) conv1 Shortcut Topology Rule up_blocks.*.resnets.*.conv1 MXFP8 E4M3, unconditionally, bypassing the κ/SNR check; ×3 per level, one per up-block ResNet. The concatenated input spans a peak-to-median channel range of 58× at the median layer and up to 163× (~1.4× an ordinary conv). W₄/W₈ Weight Quantization (Offline) Per-output-channel format selection. input channel output channel W8: INT8-sym, INT8-asym, MXINT8 W4: INT4-sym, INT4-asym, NF4, FP4 E2M1, MXINT4, MXFP4 E2M1 372 quantized conv and linear layers; attention Q/K/V andconv_in/conv_outstay FP16. Few-Step Variant (SDXL-Turbo) • same UNet topology; 1 denoising step at 512 × 512 • weights: Chameleon adaptive palette • activations: MixDQ static scales + mixed precision • MixDQ's BOS-aware bypass dropped • concat: 9 up-block conv_shortcutlayers stay FP16; no MXFP8 pin c Skip Concatenation Channel-wisetorch.catof the decoder stream (from below) with one encoder skip, before each of the three up-block ResNets. Per level, the skips are the two ResNet outputs of the same-level encoder block and the downsampled output of the level above ( conv_in's output at the top). Both conv1(pinned to MXFP8) and the parallel 1×1 conv_shortcut(routed by κ/SNR) read its output. Figure 3: The UNet execution path of Chameleon (SDXL base 1.0), with the few-step variant used for SDXL-Turbo. The encoder (DownBlock2D and two CrossAttnDownBlock2Ds) descends to a cross-attention mid block and the decoder climbs back up; at every level the concate- nation c joins the decoder stream with one encoder skip before each of the three up-block ResNets – the encoder block’s two ResNet outputs and the downsampled output of the level above (conv in’s output at the top). Activations follow macro-routing with static, ahead-of-time-calibrated per-bucket scales (Q-Diffusion style), in contrast to the DiT path’s dynamic per-sample scales; the callout gives the measured share of the 372 quantized layers assigned each format in each bucket of the shipped LUT (Table 7). The nine layers matching upblocks. * .resnets. * .conv1 – the 3× 3 convolution that reads the concatenated tensor, three per level – are routed to MXFP8 E4M3 regardless of the kurtosis/SNR reading, because that tensor spans a peak-to-median per-channel magnitude range of 58× at the median layer and up to 163×; the parallel 1× 1 convshortcut reads the same tensor and is routed normally. Weights use per-output-channel format selection (Sec- tion 4.5); attention Q/K/V projections, conv in/convout and both text encoders stay in FP16. The few-step variant keeps the topology but runs one step at 512× 512: Chameleon supplies the weight palette, activations use MixDQ’s static scales and mixed-precision assignment, MixDQ’s BOS-aware bypass is dropped (Table 6), and the nine up-block convshortcut layers that read the concatenation stay in FP16, with no MXFP8 pin (Section 4.6; Appendix A.4). 18 A.5ARCHITECTURAL-FORK DIAGRAMS This appendix collects the schematic diagrams for the execution paths of the architectural fork (Sec- tion 4.6 of the main paper). Figure 4 shows the DiT path used for PixArt-α, and Figure 3 shows the UNet path used for SDXL together with the few-step modifications used for SDXL-Turbo. A.6CLIP-SCORE COMPUTATION Caption alignment: Each generated image must be scored against the caption it was gener- ated from. Every per-backbone generator builds its prompt list as the flat list of raw anno- tations from captions val2014.json shuffled with a fixed seed (42), and writes image i to i:05d.png; the scorer reconstructs the identical list and pairs idx:05d.png with prompts[idx]. Because the shuffle seed and the ordering convention are shared by all six gen- erators and by every baseline, every configuration is scored against exactly the same captions in the same order, and the comparison across rows of Table 1 is like-for-like. DiT Block × 28 LayerNorm + modulate Self-Attention (attn1) Cross-Attention (attn2) LayerNorm + modulate Feed-Forward (MLP) + + + × ×gate_msa × ×gate_mlp Noisy VAE latent, 4 × 128 × 128 Patchify (patch size 2) Sequence: 4096 tokens × 1152 dim adaln_single(FP16) Timestep t Timestep embedding AdaLN-single (t, resolution, aspect ratio) one global MLP, shared by all 28 blocks; summed with each block'sscale_shift_table Caption projection T5 text embedding (4096-d, 120 tokens) K/V Final LayerNorm + modulate Linear (proj_out) Unpatchify Predicted noise (epsilon-hat) A₈ Activation Quantization (Runtime) Macro-routing format code per (layer, timestep bucket) Timestep Bucket Format Code clean signal (low t) pure noise (high t) T1FP8 E5M2 98% T2FP8 E5M2 98% T3FP8 E5M2 97% T4FP8 E5M2 97% T5FP8 E5M2 100% T6FP8 E5M2 100% T7FP8 E5M2 100% T8FP8 E5M2 100% T9FP8 E5M2 100% T10FP8 E5M2 100% one LUT read per layer per step INT8-asym never selected: unlike the UNet, DiT activations stay heavy-tailed at every timestep Micro-scaling scale computed dynamically from the current tensor's min/max at inference W₄ Weight Quantization (Offline) Per-linear joint (g, f) search. 288 192 128 64 32 INT4-asym NF4 FP4 E2M1 Group size (g) Format (f) g = 32 for all 282 layers; INT4-asym 213, NF4 69, FP4 E2M1 0 argmax Input-channel grouping (along C_in) 282 quantized linears (28 × 10 + caption projection); proj_outandadaln_singlestay FP16. Figure 4: The DiT execution path of Chameleon (PixArt-α XL/2, 28 blocks). There is no shortcut concatenation of the kind the UNet carries, so the topology-driven MXFP8 rule of Section 4.6 is dropped. Weights: every n.Linear in the self-attention, cross-attention and feed-forward sub-layers, together with the two captionprojection linears (282 in total; projout and adalnsingle are kept in FP16) enters a joint (g,f ) search over group sizes g ∈32, 64, 128, 192, 288 and formats f ∈INT4-asym,NF4,FP4 E2M1 at 4 bits, scored by an input-aware SNR that weights each input channel’s squared error by its activation energy from a 16-prompt pre-pass (it settles on g = 32 everywhere, with INT4-asym for 213 linears and NF4 for 69); the search is per-linear, groups run along the input-channel dimension, and it runs entirely offline. Activations: macro-routing (the per-bucket format LUT of equation 2) composed with per- tensor dynamic per-sample scaling. The bucket-to-format assignment shown is the calibrated LUT for this model: FP8 E5M2 wins in 97–100% of the 282 linears in every bucket and INT8-asym is never selected, so the three-phase progression of Appendix A.3 does not occur on the DiT. Ap- pendix A.9.5 reports the full statistics. The format is fixed at calibration time, but the scale is computed dynamically from the current tensor’s range at inference, following Q-DiT’s observation that DiT activations shift drastically across samples. 19 We flag this explicitly because an earlier version of our scorer built its caption list differently – one caption per image identifier, unshuffled – so that image i was scored against an unrelated caption. The resulting values measured image-versus-random-caption similarity, clustered near cosine 0.075, and did not preserve the ordering across configurations: the two most degraded ablation arms in Appendix A.9 recorded the highest scores. The released scorer reproduces the generators’ caption list verbatim, and we verified equality across all 24,576 indices before recomputing every number reported here. A.7ALGORITHM PSEUDOCODE This appendix provides the full pseudocode for the algorithms summarized in the main paper. Al- gorithm 1 is the offline calibration loop referenced in Section 4.4; Algorithm 2 is the runtime fake- quantization dispatch of the UNet and few-step paths referenced in Section 4.7; Algorithm 3 is the corresponding dispatch for the DiT path, which replaces the calibrated scale with a per-sample one (Section 4.6). Algorithms 1 and 3 both invoke a shared helper ScaleZP, which derives the affine parameters of a format from an observed value range: INT8-asym takes s = (hi−lo)/255 and z = round(−lo/s); FP8 E4M3 and E5M2 take s = max(|lo|,|hi|) divided by 448 and 57344 respectively, with z = 0; the MX formats take s = 1, since the shared block exponent supplies the scaling. The difference between the two runtime paths is precisely when this helper is called: the UNet path calls it once per (layer, bucket) at calibration time and stores the result, while the DiT path calls it on every forward pass from the current tensor’s own range. Algorithm 1 Chameleon LUT calibration Require: network N with L instrumented layers, B timestep buckets, calibration prompt set P = p 1 ,...,p K , schedule t T → t 0 , cumulative products ̄α Ensure: format LUT F ∈0,..., 4 L×B , scale LUT S ∈ R L×B , zero-point LUT Z ∈ R L×B 1: initialize n, Σ 1 , Σ 2 , Σ 3 , Σ 4 ← 0 and lo← +∞, hi←−∞, all L× B 2: for each prompt p∈ P do 3: x← random latent 4:for each step t from t T to t 0 do 5:b←⌊t/(T/B)⌋ 6:x← N.step(x,t,p)▷ standard sampling pass 7:for each instrumented layer l do 8:X ← cached input activation of l at this step 9:n[l,b] += numel(X); Σ k [l,b] += P i X k i for k = 1,..., 4 10:lo[l,b]← min(lo[l,b], min i X i ); hi[l,b]← max(hi[l,b], max i X i ) 11:end for 12:end for 13: end for 14: for each (l,b) do 15: κ[l,b]← m 4 /σ 4 , with σ 2 and m 4 recovered in closed form from n, Σ 1 ,..., Σ 4 16: t b ← b· (T/B) + (T/B)/2▷ bucket midpoint 17: F [l,b]← Route κ[l,b], SNR(t b ), is shortcut(l) ▷ Section 4.3 18: S[l,b], Z[l,b]← ScaleZP F [l,b], lo[l,b], hi[l,b] 19: end for Implementation notes: Two notes from Section 4.7 matter for reproducing Algorithms 2 and 3. (i) The LUT and scale tables are registered as PyTorch buffers, not parameters, so they move with the module across devices and serialize with the state dict. The format branch is data-dependent only in appearance: f is constant for any given (layer, bucket), so a specializing compiler can in principle hoist the dispatch out of the inner loop. Our released implementation does not rely on this – it reads the code from the buffer at each step – and we leave the compiled runtime to future work. (i) FP8 round-trips clamp to the format’s representable range before the cast. Without clamping, values above 448 map to NaN bit patterns in E4M3 (which does not have ±∞), and values above 57344 map to±∞ in E5M2, which then becomes NaN through the∞−∞ that subsequent norm 20 Algorithm 2 DynamicTimestepFakeQuantize.forward(x,t) – UNet and few-step paths 1: if not enabled then return x▷ pre-calibration pass-through 2: end if 3: b← min ⌊t/bucket size⌋, B− 1 4: (f,s,z)← LUT[layerid,b]▷ one tensor-indexed read 5: if f = 0 then return fq int8asym(x,s,z) 6: else if f = 1 then return fqfp8e4m3(x,s) 7: else if f = 2 then return fq fp8e5m2(x,s) 8: else if f = 3 then return fqmxfp8e4m3(x,blocksize=32) ▷ MX: block exponent, s unused 9: else if f = 4 then return fq mxint8(x,blocksize=32) ▷ in the code space; not emitted by Route 10: end if Algorithm 3 ChameleonDiTDynamicQuantize.forward(x,t) – DiT path 1: if not enabled then return x 2: end if 3: b← min ⌊t/bucketsize⌋, B− 1 4: f ← formatlut[layerid,b]▷ macro-routing: format only 5: lo, hi← min(x), max(x)▷ micro-scaling: per-sample, per-forward 6: s,z ← ScaleZP(f, lo, hi) 7: return fq f (x,s,z) layers compute, and the model produces black images. This was the single most painful bug in our implementation, and we mention it because every quantization codebase we have read gets it wrong. Calibration cost: Table 2 reports the end-to-end cost of Algorithm 1 for each backbone (Sec- tion 5.3). Table 2: End-to-end calibration cost on a single A100 80 GB in fake-quant mode, with 128 cal- ibration prompts and B = 10 buckets. The reported LUT size includes the per-(layer, bucket) format and scale tables; for SDXL and PixArt-α the larger figure additionally includes the per- output-channel weight-format metadata. SDXL-Turbo is an order of magnitude cheaper because its one-step schedule leaves no timestep axis to route over: calibration reduces to a weight-only format search with no calibration forward passes (Section 4.6). The three runs total 53 m 42 s. ModelCalib timePeak GPU mem LUT size SDXL UNet45 m 16 s11.44 GB 252 KB (act. only) / 18 MB JSON of weight formats (≈1 MB at one byte per channel) SDXL-Turbo1 m 01 s9.63 GB157 KB (single config file) PixArt-α7 m 25 s18.27 GB93 KB (per-layer (g,f ) + LUT) A.8ON CHAMELEON FID BELOW THE FP16 REFERENCE Every Chameleon configuration in Table 1 reports a FID below its unquantized FP16 reference. The effect spans an order of magnitude in size, from −0.34 on SDXL-Turbo at W 4 A 8 (21.29 against 21.63) to−5.39 on PixArt-α at W 4 A 8 (22.24 against 27.63), and it appears on all three backbones at both bit-widths. The reading is unusual – one would normally expect the unquantized model to dominate – so we record what we can and cannot establish about it. The effect exceeds measurement noise: FID is computed on the full 24,576-image generation against the 40,504-image COCO-2014 reference set. Two independently calibrated runs of an iden- tical configuration differ by 0.04 FID (Appendix A.9), so inversions spanning 0.34 to 5.39 are not 21 attributable to calibration or sampling variance. Nor are they confined to a single fork: they appear under three different weight-selection procedures (per-output-channel SNR on SDXL, the adaptive palette over MixDQ activations on SDXL-Turbo, and the joint (g,f ) search on PixArt-α) and under both static and dynamic activation scaling. The mechanism is not uniform smoothing: A natural explanation is that aggressive rounding attenuates the very-high-frequency texture that the InceptionV3 features underlying FID over- penalize relative to perceptual quality – an effect documented in the GAN compression literature, where pruning and quantization occasionally improve FID for this reason. We tested it directly by measuring the variance of the Laplacian over 400 prompt-matched images per configuration (Table 8). The explanation holds on PixArt-α, where quantization reduces high-frequency energy from 1287 to 1057 – and that is also the backbone with the largest inversion. It does not hold for the two UNet backbones, where the quantized models carry substantially more high-frequency content than their FP16 references (522 → 662 on SDXL, 439 → 725 on SDXL-Turbo). Whatever produces the inversion there, it is not a low-pass effect, and we do not have a validated account of it. Bottom line for the main-text claims: We report the inversions as raw measurements and make no stronger claim. Because they are measured on a single feature extractor with known frequency biases, and because we can rule out the most obvious mechanism on two of three backbones, a reader skeptical of FID as a single-number metric should treat the quantized configurations as occupying the same neighborhood as their FP16 references rather than as strictly superior. We note that the corrected CLIP scores of Appendix A.6 move in the same direction on two of three backbones – Chameleon exceeds the FP16 reference at W 4 A 8 on SDXL-Turbo (26.85 against 26.63) and PixArt-α (26.09 against 25.99) – but establishing a genuine quality improvement over FP16 would require a perceptual metric such as human preference, which we have not run. A.9ABLATIONS Each arm in this appendix generates 5,000 images from the same seed-42 COCO prompt subset and is scored with the clean-FID and CLIP pipeline of Appendix A.4. The ablation study is self- contained: all arms share a common baseline generated from the same calibration cache, and that baseline (19.39) is not numerically identical to the SDXL W 4 A 8 row of Table 1, which is a sub- score of the 24,576-image run. Comparisons should therefore be read within this appendix rather than against the main table. Two independently calibrated runs of the same configuration (both default in Table 3 and B = 10 in Table 5) differ by 0.04 FID. We take this as the empirical noise floor induced by calibration sampling, and treat differences at or below it as indistinguishable. Across the twenty arms, FID and CLIP are strongly anti-correlated (r =−0.88), as they should be when lower FID and higher CLIP both indicate better output. The two configurations that collapse – single int8 at 180.51 FID and macroonly at 174.42 – record the lowest CLIP scores in the study (22.87 and 15.91 against 25.6–26.7 for every healthy arm). We note this because it is a useful check on the scoring pipeline itself: under the caption misalignment described in Appendix A.6, these same twenty arms gave r = +0.93, with the two collapsed configurations scoring highest. A.9.1ROUTING SIGNALS Table 3: Contribution of each routing statistic (SDXL W 4 A 8 , 5,000 images). ArmChangeFID↓∆CLIP↑ bothdefault κ and SNR (shipped)19.39–26.58 bothperturbed κ gates (3, 5)→ (3.5, 5.5)19.41+0.0226.55 kurtonly SNR gate disabled19.60+0.2126.59 snronlyκ frozen at 4 (mid-band)19.68+0.2926.38 singlee4m3no routing, FP8 E4M3 everywhere20.29+0.9026.48 22 Routing is worth 0.90 FID over the best single fixed format, and neither statistic alone recovers it: removing the SNR gate costs 0.21 and freezing κ costs 0.29, so the two signals carry complementary information. The perturbation arm moves the kurtosis thresholds by +17% and +10% respectively and changes FID by 0.02, just below the noise floor – the thresholds are not tuned quantities. A.9.2FORMAT PALETTE Table 4: Contribution of individual formats (SDXL W 4 A 8 , 5,000 images). drop mxfp8 removes the only format the shortcut rule of Section 4.6 can select, and therefore disables that rule. ArmChangeFID↓∆CLIP↑ fullpaletteshipped19.39–26.58 dropnf4 NF4 removed (weights)19.46+0.0726.56 drop mxfp8 MXFP8 removed (shortcut rule off)19.54+0.1526.56 dropmxfp4 MXFP4 E2M1 removed (weights)19.77+0.3826.60 single e4m3forced E4M3, shortcuts included20.29+0.9026.48 singleint8forced INT8-asym, shortcuts included180.51+161.1222.87 Every format earns its place, though not equally: dropping MXFP4 E2M1 costs 0.38 and dropping NF4 only 0.07. Disabling the shortcut rule costs 0.15, which is the price of the topology-driven MXFP8 assignment on nine layers. The decisive row is singleint8: forcing uniform integer quantization on every layer at every timestep raises FID by an order of magnitude (19.39→ 180.51) and produces over-saturated, structurally intact but visually destroyed images. This is the failure mode the framework exists to avoid, and it is what separates format routing from scale tuning – no choice of INT8 scale recovers it. A.9.3TIMESTEP BUCKET COUNT Table 5: Sensitivity to the number of timestep buckets (SDXL W 4 A 8 , 5,000 images). Each B is calibrated independently. BFID↓CLIP↑ 119.4726.58 519.4126.57 10 (shipped)19.3526.72 2019.5926.53 FID varies little with B: the total spread is 0.24 over a twentyfold range of bucket counts. The shipped B = 10 is the best setting on both metrics, but the margins are small. Collapsing the schedule to a single bucket (B = 1, which reduces the router to one static format per layer) costs 0.12 FID and 0.14 CLIP; B = 5 lies between the two; and B = 20 is the worst of the four. The calibrated LUT explains the flatness (Appendix A.9.5): on SDXL there are only three distinct temporal regimes, so once B resolves them the extra buckets largely replicate their neighbors, while B = 20 spreads the same 128 calibration trajectories over twice as many windows and the per- bucket moments get noisier. The two axes are therefore separable, and unequal: measured against the best single fixed format (singlee4m3, 20.29 in Table 3), the per-layer assignment at B = 1 already recovers 0.82 FID and the timestep axis adds the remaining 0.12. Both tables’ shipped runs differ by 0.04 (below), so that split is approximate; what it does show is that per-tensor format choice carries the gain and temporal granularity refines it. A.9.4ARCHITECTURAL-FORK ADDITIONS The two DiT rows separate the fork’s two mechanisms and show they are strongly asymmetric. Freezing the per-sample scale collapses generation entirely (+145 FID), confirming Q-DiT’s obser- vation that DiT activations shift too much across samples for any static scale; dynamic per-sample scaling is load-bearing. Replacing the temporal LUT with a single fixed format costs 0.69, a real 23 Table 6: The per-family additions of Section 4.6 (5,000 images each). macroonly freezes the per-sample activation scale after the first observation (format LUT still active); microonly keeps the dynamic scale but flattens the LUT to one format. FamilyArmChangeFID↓∆CLIP↑ SDXL-Turbo W 8 A 8 baqoffshipped26.78–26.56 baqonfaithful BAQ re-enabled26.89+0.1126.61 PixArt-α W 4 A 8 macro+microshipped29.15–25.65 micro only LUT flattened to E4M329.84+0.6925.83 macroonlyscale frozen after first observation 174.42+145.2715.91 but secondary contribution. That ordering – per-sample adaptivity dominant, temporal granularity secondary – matches the bucket sweep on SDXL, where the timestep axis is worth 0.12 FID against the per-layer choice’s 0.82. CLIP does not resolve these rows – micro only scores 0.18 higher despite the worse FID – which is consistent with the temporal LUT on PixArt-α being close to uniform in the first place (Appendix A.9.5). For the few-step fork, re-enabling a faithful equivalent of MixDQ’s BOS-aware bypass leaves quality essentially unchanged, and the two metrics disagree on its sign: FID rises by 0.11 while CLIP rises by 0.05. Neither movement supports a benefit from the bypass. What it does carry is a cost – MixDQ’s BAQ substitutes a precomputed output for position 0 of the batch, which forces batch- size-one inference. Under Chameleon’s adaptive weight palette the BOS outlier no longer requires a bespoke mechanism to absorb it, so we drop the bypass and recover batched inference at no measurable quality cost. A.9.5WHAT THE CALIBRATED LUT ACTUALLY SELECTS Table 7: Per-bucket activation-format distribution in the shipped LUTs (B = 10). SDXL: 372 quantized layers; PixArt-α: 282. Bucket mean SNR(t) is computed from each model’s own noise schedule. Bucket b is labelled T b+1 in Figures 3 and 4. SDXL (scaled-linear) PixArt-α (linear) b SNR INT8 E4M3 E5M2 MXFP8 SNR E4M3 E5M2 057.79.9%50.3%37.4%2.4%304.52.5%97.5% 15.1412.1%48.4%37.1%2.4%4.182.5%97.5% 22.1311.6%49.2%36.8%2.4%1.162.8%97.2% 31.05–61.3%36.3%2.4%0.413.2%96.8% 40.54–62.4%35.2%2.4%0.15–100% 50.28–61.6%36.0%2.4%0.05–100% 60.14–97.6%2.4%0.02–100% 70.06–97.6%2.4%0.004–100% 80.03–97.6%2.4%0.001–100% 90.01–97.6%2.4%0.000–100% Table 7 reports what calibration actually chose, and the SDXL column tracks the routing rule of Section 4.3 exactly. INT8 appears only in buckets 0–2, precisely the buckets whose mean SNR(t) exceeds the τ high = 2 gate, and disappears at b = 3 where SNR falls to 1.05. E5M2 saturates at 97.6% from b = 6 onward, precisely where SNR < τ low = 0.2 forces Phase 1. MXFP8 holds a constant 2.4% in every bucket: this is 9/372, the nine shortcut convolutions pinned by topology, and its flatness across b is the signature of a rule that never consults a statistic. The three temporal regimes visible here (b≤ 2, 3≤ b≤ 5, b≥ 6) are also why the bucket sweep is flat: B = 5 already resolves them. The PixArt-α column is markedly less diverse. Its linear β schedule decays SNR roughly two orders of magnitude faster, so the τ low gate fires from b = 4 onward rather than b = 6, and the 24 remaining buckets are pushed to E5M2 by kurtosis; the resulting LUT is 97–100% E5M2 throughout, effectively uniform. We state this plainly: on PixArt-α the temporal component of the routing is close to degenerate, and the gains reported in Section 5.2 come from the weight side – group-wise INT8-asym at g = 32 for 8 bits and the joint (g,f ) search at 4 bits – together with the dynamic per-sample scaling isolated in Table 6. The routing machinery is still correct on this backbone, but its degrees of freedom are not exercised; the same fixed thresholds behave differently only because SNR(t) is a property of the schedule, not of the method. A.10QUALITATIVE SAMPLES Figure 5 shows four prompts per backbone for the FP16 reference, the state-of-the-art PTQ baseline, and Chameleon at W 4 A 8 ; Table 8 quantifies the high-frequency detail visible in it. Table 8: High-frequency detail retention, measured as the Variance of the Laplacian (VL), a standard image sharpness and focus measure (Pech-Pacheco et al., 2000; Pertuz et al., 2013), over 400 images per configuration. Images are matched by filename across configurations, so every row compares the same prompts under the same seeds. Higher values indicate more high-frequency content; the FP16 column is the unquantized reference for that backbone, not a target to exceed. FamilyBackbone FP16 PTQ baselineChameleon UNet diffusion SDXL522605662 Few-step distilled SDXL-Turbo439605725 Diffusion transformer PixArt-α128710301057 As visible across the grid, on all model architectures, Chameleon retains more high-frequency detail than the competing PTQ baseline. Table 8 quantifies this over 400 prompt-matched images per configuration using the VL 3 : Chameleon reaches 662 against Q-Diffusion’s 605 on SDXL, 725 against MixDQ’s 605 on SDXL-Turbo, and 1057 against Q-DiT’s 1030 on PixArt-α. A.11NUMBER-FORMAT DETAILS This appendix expands Section 4.2 of the main paper by walking through each candidate format in Chameleon’s palette and identifying the kurtosis and SNR regimes (Appendix A.3) in which each is the per-format MSQE-minimizing choice. INT8 (asymmetric): Encodes a tensor as 256 evenly spaced bins between min and max. Bin width s = (max− min)/255. Optimal under a uniform prior; degrades quickly under heavy tails because s inflates with the outlier magnitude. FP8 E4M3: One sign bit, four exponent bits with bias 7, three mantissa bits. Representable range ±448, smallest normal 2 −6 . Mantissa precision is 2 −3 , so it cleanly resolves moderate dynamic range with reasonable bin density. FP8 E5M2: One sign, five exponent, two mantissa. Representable range±57344, smallest nor- mal 2 −14 . The five exponent bits give it nine orders of magnitude of dynamic range, which is what makes it the right answer in Phase 1. MXINT8 / MXFP8: A microscaling block of 32 elements carries one shared 8-bit exponent (E8M0); the elements themselves are stored in INT8 or FP8 respectively. The shared exponent is computed per block as E block =⌊log 2 max i |x i |⌋, so a tensor containing both 10 −3 and 10 2 val- ues can be represented without either being crushed: the relevant block selects its own exponent. Appendix A.12 records where our implementation conforms to the OCP specification and what con- formance costs. This is exactly the medicine for the wide-tailed concatenations at UNet shortcuts (58× median, up to 163× peak-to-median channel range; Figure 3). 3 We compute the measure as the variance of the 3× 3 discrete Laplacian of the grayscale image (scipy.ndimage.laplace), which is numerically equivalent to the widely used OpenCV formulation with default kernel size. 25 UNet DiffusionFew-Step DistilledDiffusion Transformer Half-Precision Float Baseline: FP16 W 16 A 16 SDXLSDXL-TurboPixArt-α State-of-the-Art Quantized Baselines: W 4 A 8 Q-DiffusionMixDQQ-DiT Ours: Chameleon W 4 A 8 ChameleonChameleonChameleon Figure 5: Qualitative comparison on four prompts at W 4 A 8 . Rows (top to bottom): FP16 refer- ence (SDXL, SDXL-Turbo, PixArt-α); per-architecture PTQ baseline (Q-Diffusion, MixDQ, Q-DiT respectively); Chameleon. Columns (left to right): model architectures (UNet Diffusion, Few-Step Distilled, Diffusion Transformer). Within each 2× 2 block, the four prompts are, in read- ing order, the cherry-red convertible, the orange tabby cat, the golden retriever puppy, and the black sports car; the prompts are given verbatim in the released code. Seeds are fixed across rows so that the same prompt index produces the same latent initialization under every quantization con- figuration. 26 INT4 / NF4 / FP4 / MXINT4 / MXFP4: At 4 bits, the choice of code matters even more. INT4 is uniform, in symmetric and asymmetric variants; NF4 (Dettmers et al., 2023) is the quantile-optimal code for a unit Gaussian; FP4 E2M1 has a bias toward small values that tracks ReLU-like sparsity (one sign, two exponent and one mantissa bit, with representable values 0,±0.5,±1,±1.5,±2,±3,±4,±6); and the two MX variants add a shared block exponent on top of a narrow integer or floating-point body. All six are available to the per-output-channel search on SDXL; the few-step fork searches all but INT4-sym per layer jointly with the group size, and the DiT fork searches the non-MX subsetINT4-asym,NF4,FP4 E2M1 jointly with the group size (Section 4.6), since an explicitly searched group size already supplies the block granularity the MX formats would otherwise contribute. For a generalized-Gaussian model of activation distributions, the per-format MSQE curves cross as a function of the kurtosis κ, near κ ≈ 3 and κ ≈ 5; we use those crossings as the kurtosis gates. The SNR gates0.2, 2.0 do not come from that model: they are read off the noise schedule, and mark where the schedule enters and leaves its noise-dominated phase. Why fixed thresholds survive different noise schedules: The backbones we evaluate use differ- ent β schedules – scaled-linear for SDXL and SDXL-Turbo, linear for PixArt-α – so SNR(t) spans ∼ 10 3 down to ∼ 10 −2 on the former and ∼ 10 4 down to ∼ 10 −4 on the latter. Applying the same gates (τ low ,τ high ) = (0.2, 2.0) therefore partitions the schedule differently: four of ten buckets fall into Phase 1 on SDXL against six of ten on PixArt-α. This is the point rather than a complication. The thresholds are stated in terms of SNR(t), which each model’s own noise schedule supplies, so they adapt to the schedule without being retuned – which is what lets the hyperparame- ter footprint stay fixed across backbones (Section 5.3). The prediction is exact: the buckets the gate marks as Phase 1 on PixArt-α (b ≥ 4) are precisely those the shipped LUT fills with 100% FP8 E5M2 (Appendix A.9.5). A.12MX CONFORMANCE AND ITS COST The OCP MX specification requires the per-block shared scale to be a power of two – an E8M0 exponent – rather than an unconstrained floating-point value. Our activation path implements this exactly: the block scale is 2 ⌊log 2 max i |x i |⌋ , so normalized values land in (−2, 2) and the simulation matches what conforming MX hardware computes. The SDXL weight-side implementation deviates, using an unconstrained per-block scale, which is strictly more expressive than the specification al- lows; the few-step path’s MX weights already use power-of-two scales, and the DiT path selects no MX weight format at all. We measured the cost of conformance directly by rounding the weight-side scale to the nearest power of two on real SDXL weights. It is 3.5 dB of SQNR – 45.4 → 41.9 for MXINT8 and 20.3 → 16.7 for MXINT4 – close to the theoretical worst case of 6 dB from forfeiting up to one bit of range. The consequence for the palette is larger than that figure suggests. Under an unconstrained scale, block-scaled MXINT8 wins essentially every output channel at 8 bits, which would make the weight palette degenerate; under E8M0 the per-channel selection of Section 4.5 distributes across INT8-asym (59%), MXINT8 (37%) and INT8-sym (4%). Conformance is therefore what makes the per-channel search meaningful at 8 bits rather than a formality. The SDXL weight-side numbers reported in this paper correspond to the unconstrained variant and should be read as an upper bound on what a conforming MX weight kernel would deliver; the activation-side numbers are conformant as reported. A.13EXTENDED DISCUSSION AND LIMITATIONS Real hardware versus fake-quant: All numbers reported in Section 5 use fake-quantization – round-trip casts inside FP16 – because real INT4/NF4/FP4/MX4 kernels are not yet uniformly available across the three backbones we evaluate. We therefore make no efficiency claims: the results characterize what the format assignment costs in fidelity, not what it saves in latency or memory. Establishing the latter would require native FP8 and MX kernels – MX being a Blackwell- class hardware feature, with FP8 already native on Hopper and Ada – and we leave a real-kernel measurement to a hardware-focused follow-up. 27 Composition with sampler adaptation: Q-Sched (Frumkin & Marculescu, 2026) keeps the quantized weights frozen and learns two scalar preconditioning coefficients per sampler step that warp the integration trajectory. Their motivation – that aggressive quantization changes the un- derlying vector field, so the sampler optimized for FP16 is no longer optimal – is orthogonal to Chameleon’s per-bucket format choice. Composing the two should be straightforward: run Chameleon’s calibration first to fix the format LUT, then run Q-Sched’s preconditioning search on top of the now-quantized weights. We have not measured this composition and leave it to future work. Image scope: The current evaluation is limited to image generation. We expect the same routing principle to carry over to video diffusion transformers – the macro physics of the diffusion schedule, and therefore the kurtosis/SNR phase structure that Chameleon exploits, is unchanged in the tempo- ral setting – but the temporal-attention layers in video DiTs introduce additional sensitivity that we have not yet characterized. Extending Chameleon to video DiTs is a natural next step. Sub-4-bit territory: We do not address W 2 or W 1 quantization. At those bit-widths the dis- crete approximation error overwhelms what any post-training routing scheme can recover, and quantization-aware training with techniques such as BinaryDM’s evolvable-basis binarizer (Zheng et al., 2025) becomes necessary. Chameleon’s calibration pass could in principle initialize such a QAT phase, but doing so is outside the scope of a PTQ paper. Large per-channel format metadata: At extreme model scale (e.g. a hypothetical 20-billion- parameter image DiT) the per-output-channel format byte starts to add measurable overhead. We expect that a per-layer format choice with per-channel scale would recover most of the benefit at a fraction of the metadata cost, since within a single conv layer the dominant format choice tends to be shared across most output channels. Calibration on out-of-distribution prompts: Our calibration uses 128 COCO captions for all three runs. We have not stress-tested generalization to dramatically different prompt distributions – for instance, calibrating on COCO and evaluating on text-rendering or hands-and-faces bench- marks. A practitioner deploying Chameleon on a domain-specific generator should re-calibrate with a domain-matched prompt set. 28 BSTATEMENTS B.1AI USE STATEMENT In this work, we used generative AI tools to implement methods. We have not used generative AI tools to generate synthetic data sets, to develop the theoretical models or conceptual frameworks underlying the method, to propose or refine hypotheses, to design or give feedback on research methodology or experiments, to support qualitative or thematic data analysis, to interpret results, to clean or reformat datasets, or for translation. The remaining tasks with required disclosure – for- mulating mathematical claims, providing critical ingredients for proving mathematical claims, and assisting in the writing of proofs – are not applicable to this work, which contains no formal proofs. Additionally, we used generative AI tools to create and edit software code, to create and modify scientific figures, to draft and edit parts of this paper, to suggest a structure for the supplementary material, to identify relevant literature, to format references, and to search for information. We have reviewed all AI-assisted work. To elaborate: the research contributions of this paper are the authors’. The central idea – treating the number format as a discrete variable indexed by (layer, timestep bucket) – the kurtosis/SNR routing rule, the architectural fork, the design of the experimental protocol and of the ablation suite, and the interpretation of every result reported here were carried out by the authors. Generative AI as- sistance was confined to implementation and exposition. On the implementation side, it was used to write and debug the ablation harness, the per-arm monkey-patch shims, the figure-generation scripts, and several corrections to the quantization code, including a bucket-count propagation bug and a caption-alignment bug in the CLIP scorer (Appendix A.6). It was also used to compute the auxiliary measurements reported in Appendices A.10 and A.9, such as the Laplacian sharpness statistics and the FID–CLIP correlation; the authors specified what to measure and drew the con- clusions from the output. Each AI-assisted code change was validated against generated artifacts before use – for instance by byte-comparing images across ablation arms to confirm that a patch had a non-trivial effect – and every claim in AI-drafted text was checked by the authors against the artifacts on disk, with a number of claims removed or weakened as a result. Literature identified with AI assistance was verified against primary sources. We take responsibility for the final content of this work, including all text, claims, and artifacts produced with the aid of generative AI. B.2ETHICS STATEMENT This work studies post-training quantization of existing, publicly released text-to-image diffusion models. It involves no human subjects, no personally identifying information, and no new data collection: all evaluation uses the public COCO-2014 validation set (Lin et al., 2014) and publicly released model checkpoints under their respective licenses. Our method inherits the characteristics of the models it compresses. Text-to-image diffusion models are known to reproduce social biases present in their training data and can be used to generate misleading or harmful imagery. Quantization does not introduce these properties, but neither does it remove them, and we did not evaluate whether format routing shifts a model’s behavior on safety- relevant prompts – our evaluation measures distributional fidelity and prompt adherence only. A practitioner deploying a quantized model should not assume that safety evaluations performed on the full-precision model transfer unchanged. The intended benefit of this work is to reduce the memory and compute required to run these models, which lowers the barrier to on-device inference and reduces the energy cost of deployment. We note the dual-use character of that benefit: the same reduction makes generative models easier to deploy for misuse, and easier to run outside the monitoring that a hosted service provides. We judge the efficiency and accessibility benefits to outweigh this risk for a method that adds no capability beyond what the underlying models already have. B.3REPRODUCIBILITY STATEMENT We will release the framework code together with the per-model calibration artifacts – weight-format configurations and activation LUTs for all three backbones at both bit-widths – so that every number 29 in Section 5 can be reproduced without repeating calibration. Their layout and sizes are given in Table 2. Environment: All experiments run on a single NVIDIA A100 80 GB (driver 580.159.03) un- der Python 3.12, PyTorch 2.11 with CUDA 13.0, diffusers 0.37.1, transformers 5.5.4, clean-fid 0.1.35, NumPy 2.4 and SciPy 1.17. The three backbones are public checkpoints used without fine-tuning: SDXL base 1.0, SDXL-Turbo, and PixArt-α XL/2 1024-MS. Prompts and seeds: Evaluation uses the COCO-2014 validation set (Lin et al., 2014). Ev- ery generator and every baseline builds its prompt list identically – the flat annotation list from captions val2014.json shuffled with seed 42 – and writes image i toi:05d.png, with the latent seed fixed at the global prompt index. A given index therefore selects the same caption, the same latent initialization, and the same scored caption under every configuration, so all comparisons in Table 1 and Appendix A.9 are like-for-like. Reproducing the main table: Each row of Table 1 is one generation call followed by one scor- ing call. For the Chameleon rows, the calibration artifacts are loaded rather than recomputed, for example python chameleon_generation.py --weight-bits 4 \ --num-samples 24576 --num-inference-steps 50 --batch-size 16 \ --coco-captions captions_val2014.json \ --load-weights sdxl_w4a8_weights.pt \ --load-activation-lut sdxl_w4a8_lut.pt \ --output-dir <out> with the per-backbone step counts, guidance scales and resolutions of Appendix A.4. Baselines are invoked through their own generators at the settings their authors specify; we note in particular that MixDQ’s W 4 A 8 configuration is a per-layer mixed-precision assignment averaging four bits, supplied as a YAML configuration, rather than uniform 4-bit quantization. Every ablation arm in Appendix A.9 is a single entry in the released dispatcher, which applies one monkey-patch to the shipped code path and reruns generation and scoring unchanged. Calibration: Calibration uses 128 prompts, B = 10 timestep buckets, a 20-step trajectory per prompt, and no gradient updates anywhere. The procedure is given as pseudocode in Appendix A.7 and its end-to-end cost in Table 2: under an hour for all three backbones combined. Scoring: We report clean-FID (Parmar et al., 2022) computed on the full 24,576-image genera- tion against the complete 40,504-image val2014 reference set, and CLIP-score with ViT-L/14 (Radford et al., 2021) against the caption each image was generated from; the scorer reconstructs the generators’ shuffled caption list verbatim (Appendix A.6). Sharpness measurements in Ap- pendix A.10 use the variance of the 3× 3 discrete Laplacian of the grayscale image. Known deviations: Two properties of the implementation should be noted by anyone reproducing or extending this work. All results use fake-quantization – round-trip casts inside FP16 – rather than low-precision kernels, so they characterize fidelity and not speed (Appendix A.13). And on SDXL our weight-side MX implementation uses an unconstrained per-block scale rather than the power- of-two E8M0 exponent the OCP specification requires (the few-step path already conforms, and the DiT path selects no MX weight format); Appendix A.12 quantifies what conformance would cost. 30