```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline

_cpp_source = r"""
#include <torch/extension.h>

torch::Tensor fused_mish_epilogue(
    torch::Tensor x, double add_value, double scale);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/OpMathType.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>
#include <algorithm>
#include <cstdint>

__device__ __forceinline__ float activate(
    float x, float add_value, float scale) {
    const float softplus = x > 20.0f ? x : log1pf(expf(x));
    float y = x * tanhf(softplus);
    y = y + add_value;
    y = y < -1.0f ? -1.0f : y;
    y = y > 1.0f ? 1.0f : y;
    return y * scale;
}

__global__ void fused_float4_kernel(
    const float* __restrict__ x,
    float* __restrict__ out,
    int64_t n,
    float add_value,
    float scale) {
    const int64_t tid =
        static_cast<int64_t>(blockIdx.x) * blockDim.x + threadIdx.x;
    const int64_t step =
        static_cast<int64_t>(blockDim.x) * gridDim.x;
    const int64_t vectors = n / 4;

    const float4* x4 = reinterpret_cast<const float4*>(x);
    float4* out4 = reinterpret_cast<float4*>(out);

    for (int64_t i = tid; i < vectors; i += step) {
        const float4 v = x4[i];
        float4 r;
        r.x = activate(v.x, add_value, scale);
        r.y = activate(v.y, add_value, scale);
        r.z = activate(v.z, add_value, scale);
        r.w = activate(v.w, add_value, scale);
        out4[i] = r;
    }

    for (int64_t i = vectors * 4 + tid; i < n; i += step) {
        out[i] = activate(x[i], add_value, scale);
    }
}

__device__ __forceinline__ float softplus_value(float x) {
    return x > 20.0f ? x : log1pf(expf(x));
}

__device__ __forceinline__ double softplus_value(double x) {
    return x > 20.0 ? x : log1p(exp(x));
}

__device__ __forceinline__ float tanh_value(float x) {
    return tanhf(x);
}

__device__ __forceinline__ double tanh_value(double x) {
    return tanh(x);
}

template <typename scalar_t>
__global__ void fused_generic_kernel(
    const scalar_t* __restrict__ x,
    scalar_t* __restrict__ out,
    int64_t n,
    double add_value,
    double scale) {
    using acc_t = at::opmath_type<scalar_t>;

    const int64_t tid =
        static_cast<int64_t>(blockIdx.x) * blockDim.x + threadIdx.x;
    const int64_t step =
        static_cast<int64_t>(blockDim.x) * gridDim.x;
    const acc_t add = static_cast<acc_t>(add_value);
    const acc_t factor = static_cast<acc_t>(scale);

    for (int64_t i = tid; i < n; i += step) {
        const acc_t v = static_cast<acc_t>(x[i]);
        const scalar_t mish = static_cast<scalar_t>(
            v * tanh_value(softplus_value(v)));

        // Preserve the intermediate rounding of separate PyTorch operators.
        const scalar_t added =
            static_cast<scalar_t>(static_cast<acc_t>(mish) + add);
        acc_t y = static_cast<acc_t>(added);
        y = y < acc_t(-1) ? acc_t(-1) : y;
        y = y > acc_t(1) ? acc_t(1) : y;
        out[i] = static_cast<scalar_t>(y * factor);
    }
}

torch::Tensor fused_mish_epilogue(
    torch::Tensor x, double add_value, double scale) {
    TORCH_CHECK(x.is_cuda(), "Expected a CUDA tensor");
    TORCH_CHECK(x.is_contiguous(), "Expected a contiguous tensor");

    const c10::cuda::CUDAGuard device_guard(x.device());
    auto out = torch::empty_like(x);
    const int64_t n = x.numel();
    if (n == 0) {
        return out;
    }

    constexpr int threads = 256;
    const auto stream = at::cuda::getCurrentCUDAStream();

    if (x.scalar_type() == at::ScalarType::Float &&
        reinterpret_cast<uintptr_t>(x.data_ptr<float>()) % 16 == 0) {
        const int64_t work = (n + 3) / 4;
        const int blocks = static_cast<int>(
            std::min<int64_t>((work + threads - 1) / threads, 4096));

        fused_float4_kernel<<<blocks, threads, 0, stream>>>(
            x.data_ptr<float>(),
            out.data_ptr<float>(),
            n,
            static_cast<float>(add_value),
            static_cast<float>(scale));
    } else {
        const int blocks = static_cast<int>(
            std::min<int64_t>((n + threads - 1) / threads, 4096));

        AT_DISPATCH_FLOATING_TYPES_AND2(
            at::ScalarType::Half,
            at::ScalarType::BFloat16,
            x.scalar_type(),
            "fused_mish_epilogue",
            [&] {
                fused_generic_kernel<scalar_t>
                    <<<blocks, threads, 0, stream>>>(
                        x.data_ptr<scalar_t>(),
                        out.data_ptr<scalar_t>(),
                        n,
                        add_value,
                        scale);
            });
    }

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return out;
}
"""

_fused_ops = load_inline(
    name="conv_transpose_mish_hardtanh_epilogue",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["fused_mish_epilogue"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3", "--fmad=false"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(
        self,
        in_channels,
        out_channels,
        kernel_size,
        stride,
        padding,
        output_padding,
        add_value,
        scale,
    ):
        super().__init__()
        self.conv_transpose = nn.ConvTranspose2d(
            in_channels,
            out_channels,
            kernel_size,
            stride,
            padding,
            output_padding,
        )
        self.add_value = add_value
        self.scale = scale

    def forward(self, x):
        x = self.conv_transpose(x)
        return _fused_ops.fused_mish_epilogue(
            x.contiguous(), float(self.add_value), float(self.scale)
        )
```