```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_postprocess_cuda(
    torch::Tensor x, torch::Tensor sum_tensor);
"""

_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>

struct BroadcastInfo {
    int64_t sizes[5];
    int64_t strides[5];
};

__device__ __forceinline__ float gelu_exact(float x) {
    return (0.5f * x) *
           (1.0f + erff(x * 0.70710678118654752440f));
}

__device__ __forceinline__ double gelu_exact(double x) {
    return (0.5 * x) *
           (1.0 + erf(x * 0.70710678118654752440));
}

template <typename scalar_t, bool ChannelOnly>
__global__ void fused_postprocess_kernel(
    scalar_t* __restrict__ x,
    const scalar_t* __restrict__ addition,
    int64_t count,
    int64_t channels,
    int64_t spatial,
    BroadcastInfo info)
{
    using acc_t = at::opmath_type<scalar_t>;

    const int64_t step = int64_t(blockDim.x) * gridDim.x;
    for (int64_t i = int64_t(blockIdx.x) * blockDim.x + threadIdx.x;
         i < count; i += step) {
        int64_t offset;
        if (ChannelOnly) {
            offset = (i / spatial) % channels;
        } else {
            offset = 0;
            int64_t remaining = i;
            #pragma unroll
            for (int d = 4; d >= 0; --d) {
                const int64_t coordinate = remaining % info.sizes[d];
                remaining /= info.sizes[d];
                offset += coordinate * info.strides[d];
            }
        }

        acc_t value = static_cast<acc_t>(x[i]);
        value = value > acc_t(0) ? value : value * acc_t(0.2);

        // Preserve the intermediate rounding of separate PyTorch operators.
        value = static_cast<acc_t>(static_cast<scalar_t>(value));
        value += static_cast<acc_t>(addition[offset]);
        value = static_cast<acc_t>(static_cast<scalar_t>(value));

        value = value < acc_t(-1) ? acc_t(-1) : value;
        value = value > acc_t(1) ? acc_t(1) : value;
        x[i] = static_cast<scalar_t>(gelu_exact(value));
    }
}

torch::Tensor fused_postprocess_cuda(
    torch::Tensor x, torch::Tensor sum_tensor)
{
    TORCH_CHECK(x.is_cuda() && sum_tensor.is_cuda(),
                "Expected CUDA tensors");
    TORCH_CHECK(x.device() == sum_tensor.device(),
                "Tensors must share a device");
    TORCH_CHECK(x.scalar_type() == sum_tensor.scalar_type(),
                "Tensors must share a dtype");
    TORCH_CHECK(x.dim() == 5 && x.is_contiguous(),
                "Expected contiguous NCDHW convolution output");

    const c10::cuda::CUDAGuard guard(x.device());
    const auto broadcast = sum_tensor.expand_as(x);

    BroadcastInfo info{};
    for (int d = 0; d < 5; ++d) {
        info.sizes[d] = x.size(d);
        info.strides[d] = broadcast.stride(d);
    }

    const bool channel_only =
        info.strides[0] == 0 &&
        info.strides[1] == 1 &&
        info.strides[2] == 0 &&
        info.strides[3] == 0 &&
        info.strides[4] == 0;

    const int64_t count = x.numel();
    if (count == 0) return x;

    constexpr int threads = 256;
    const int blocks = static_cast<int>(
        std::min<int64_t>((count + threads - 1) / threads, 65535));
    const int64_t channels = x.size(1);
    const int64_t spatial = x.size(2) * x.size(3) * x.size(4);
    const auto stream = at::cuda::getCurrentCUDAStream();

    AT_DISPATCH_FLOATING_TYPES_AND2(
        at::ScalarType::Half, at::ScalarType::BFloat16,
        x.scalar_type(), "fused_conv3d_postprocess", [&] {
            if (channel_only) {
                fused_postprocess_kernel<scalar_t, true>
                    <<<blocks, threads, 0, stream>>>(
                        x.data_ptr<scalar_t>(),
                        broadcast.data_ptr<scalar_t>(),
                        count, channels, spatial, info);
            } else {
                fused_postprocess_kernel<scalar_t, false>
                    <<<blocks, threads, 0, stream>>>(
                        x.data_ptr<scalar_t>(),
                        broadcast.data_ptr<scalar_t>(),
                        count, channels, spatial, info);
            }
        });

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return x;
}
"""

_fused_ops = load_inline(
    name="conv3d_leaky_add_clamp_gelu_fused",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["fused_postprocess_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(self, in_channels, out_channels, kernel_size, sum_tensor_shape):
        super().__init__()
        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)
        self.sum_tensor = nn.Parameter(torch.randn(sum_tensor_shape))

    def forward(self, x):
        x = self.conv(x)

        # Preserve autograd and mixed-dtype promotion when needed.
        if (
            not x.is_cuda
            or x.dtype != self.sum_tensor.dtype
            or (
                torch.is_grad_enabled()
                and (x.requires_grad or self.sum_tensor.requires_grad)
            )
        ):
            x = torch.nn.functional.leaky_relu(x, negative_slope=0.2)
            x = x + self.sum_tensor
            x = torch.clamp(x, min=-1.0, max=1.0)
            return torch.nn.functional.gelu(x)

        return _fused_ops.fused_postprocess_cuda(
            x.contiguous(), self.sum_tensor
        )
```